12. ITU G.hn: Broadband Home Networking

This chapter, focused on the G.hn multiple-input multiple-output (MIMO) power line communication (PLC) technology, is structured in the following manner:

The chapter starts with Section 12.2, giving an introduction to the G.hn family of standards which are the basis for G.hn MIMO. This includes an overview description of G.hn’s network architecture and operation, the structure of the (non-MIMO) G.hn transceiver and G.hn’s media access (MAC) scheme and an overview on G.hn’s functionalities and mechanisms.

Section 12.3 provides an introduction to G.hn MIMO, focusing on the MIMO configurations applicable to the MIMO PLC channel. This section also lists the basic requirements which were set for the design of the G.hn MIMO transceivers.

Section 12.4 describes G.hn MIMO with its various elements: First, the frame format used for MIMO transmissions is described, highlighting its design consideration aimed to allow the receiver to achieve gain, timing and frequency synchronisation along with channel estimates of the MIMO PLC channel. Following that, the section describes the G.hn MIMO transceiver structure, with the blocks added/changed compared to that of a non-MIMO G.hn transceiver: the spatial streams (SSs) parser, bit loading, Tx port mapper and more. Finally, the section describes the MIMO transmission schemes used for transmitting the payload. G.hn MIMO provides various schemes in which a G.hn MIMO transmitter can communicate with non-MIMO G.hn receivers (with enhanced performance compared to a case of a non-MIMO transmitter) and with other G.hn MIMO receivers. The latter provides three modes: Two modes use precoding in the transmitter which is based on channel state information feedback obtained from the receiver, while one mode does not require such a feedback (trade-offs between these modes are also explained). Emphasis is given to unique features, such as the ability of the receiver to control the transmitted MIMO Tx port mapping and bit loading on a subcarrier basis.

12.2 Introduction to the G.hn Standards

12.2.1 Background

Standardisation work on G.hn started in the International Telecommunication Union, Telecommunication (ITU-T) sector in 2006 with a goal to develop a next-generation home networking technology with transceivers capable of operating over all existing types of wires within homes and businesses (i.e. over power lines, phone lines and coaxial cables).

Until the introduction of G.hn, multiple home networking technologies were developed, usually by private consortia and alliances, rather than international standardisation development organisations (SDOs), where each of these technologies was usually targeting and optimised for operation over a single in-home wiring type. G.hn, on the other hand, was designed so that the transceivers and the G.hn protocols are specified in a generic way and more importantly are optimised and configurable for operation over all of the mentioned wire types (‘media’ in the G.hn jargon). The media-dependent aspect of the transceivers and protocols is specified using media-specific parameters: for example, G.hn uses an orthogonal frequency division multiplexing (OFDM) modulation, where the OFDM parameters, such as the number of subcarriers and subcarrier spacing, are defined per each media.

This unique approach, of having a unified home networking transceiver, provides multiple benefits to silicon and system vendors developing the home networking equipment and to end users (consumers) and service providers installing the home networks. These benefits include the following:

• Provides a road map/evolution path from other wired home networking technologies to a single technology

• The development of the standard leveraged from accumulated experience of member companies having a knowledge base in a multitude of existing technologies operating over the different wire types

• Simplifies the development and reduces costs for silicon vendors

• Reduced integration cost, effort and risk for systems manufacturers integrating the G.hn silicon in their design

• Simplifies implementations of equipment which allows bridging between domains operating over different media (wire types)

• Enables self-installable networks, flexible and simplified deployment architecture according to the customer’s preference. The user does not need to deal with different installation and operation procedures

G.hn MIMO, which is described in this chapter starting at Section 12.3, is adding MIMO capabilities to the G.hn transceiver in order to increase the throughput and coverage when operating over power lines.

The G.hn technology (including G.hn MIMO) is backed by the HomeGrid forum (http://www.homegridforum.org), which was formed in 2008 and, besides marketing activities aimed to promote the G.hn technology and guarantee its market success, provides a certification program for G.hn silicon and products to ensure compliance of these devices to the ITU-T. standard and interoperability between equipments of different vendors. In December 2012, the HomeGrid forum certified the first G.hn chipset (http://www.marvell.com/wireline-networking/ghn/). This chipset, by Marvell, comprises the Marvell 88LX3142 digital baseband processor and the Marvell 88LX2718 baseband analogue front end (AFE). This was followed by Sigma Designs with their G.hn chipset composed of a digital baseband chip CG5211 and AFE chip CG5213 (http://www.sigmadesigns.com/solutions_subcat.php?id=35###). Several other silicon vendors are expected to follow and have their silicon certified, for example Metanoia (http://www.metanoia.com.tw).

12.2.2 G.hn Family of Standards

The G.hn technology is specified in multiple ITU-T. standards. These standards belong to the ‘G’ family of ITU-T. standards, specifying ‘transmission systems and media, digital systems and networks’. The acronym ‘G.hn’ (‘hn’ stands for home networking) was an intermediate name given at the early stages of developing the standards and is still used as the common name for this technology. G.hn includes the following ITU-T. standards; each specifies a different part of the technology:

• G.9960: Specification of G.hn’s physical layer (PHY) and architecture. See ITU-T. 2010. G.9960.

• G.9961: Specification of G.hn’s data link layer (DLL) and security protocols. See ITU-T. 2010. G.9961 [1].

• G.9961 Amendment 1: Contains a mechanism for mitigating interferences between neighbouring G.hn domain. See ITU-T. 2012. G.9961 Amendment 1 [2].

• G.9963: Enhancement of G.hn to support MIMO (‘G.hn MIMO’) for power lines. This includes modifications to both the PHY and DLL sub-layers. See ITU-T. 2011. G.9963 [3].

• G.9964: G.hn’s power spectral density (PSD) specifications. See ITU-T. 2010. G.9964 [4].

All of the mentioned recommendations were formally approved by the ITU-T. G.9960 was the first to be approved in 2009, followed by G.9961 and G.9964 G.9963 (G.hn MIMO) was approved in December 2011.

12.2.3 G.hn Network Architecture and Topology

The architecture of G.hn home networks is illustrated in Figure 12.1. The basic G.hn network is referred to as a G.hn ‘domain’. A domain is composed of nodes connected to the same medium (wire type). In a domain, one of the nodes is acting as a ‘domain master’ (DM), while the other nodes are acting as ‘end point nodes’. The DM manages the domain: It is responsible for registering nodes, manages the transmission opportunities (TxOPs) of nodes in the domain, maintains the topology and routing information needed for relaying of management and data messages and broadcasts information to the nodes, needed for operation of the domain (e.g. information on regional masks, required frequency notches).

The G.hn domain’s architecture has the form of a mesh network, in which nodes within a domain can communicate with other nodes in that domain, either directly or via nodes acting as relay nodes. A DM is capable of supporting at least 32 registered nodes. Each node is capable of supporting simultaneous communication sessions with at least 8 other nodes.

Nodes connected to different domains (whether these domains are connected to the same or different media, i.e. wire types) generally need to communicate via inter-domain bridges (e.g. L2 or L3 bridging). The operation and specifications of such bridges is outside the scope of the G.hn standards. Nevertheless, G.hn does specify communication between domains in a specific case: G.hn includes a mechanism targeted to mitigate the interferences caused to a G.hn domain connected to power lines, by neighbouring G.hn domains operating over power lines as well. This mechanism specifies communications between the neighbouring domains in order to assist the mitigation process and to coordinate the interferers’ transmissions so that the interference is minimised.

FIGURE 12.1
G.hn home network architecture reference model.

12.2.4 G.hn Transceiver

12.2.4.1 General

The G.hn transceiver is based on a burst, windowed-OFDM modem operating with a specific frequency ‘bandplan’ (a bandplan defines the start/stop frequencies or centre frequency and the bandwidth of the transmitted signal). For each of the supported media, G.hn specifies several possible bandplans. Different OFDM parameters are specified for the different media types. However, for each media, all of the bandplans, specified for this media, are using the same subcarrier spacing. This was done in order to facilitate interoperable operation of devices of different bandplans operating over the same media which belong to the same domain. The bandplans specified in G.hn are as follows:

• For operation over power lines, three baseband bandplans are specified with bandwidth of 25 MHz (1024 subcarriers), 50 MHz (2048 subcarriers) and 100 MHz (4096 subcarriers). The frequency spacing between subcarriers is F_SC = 24.4140625 kHz.

• For phone lines, two baseband bandplans are defined: 50 MHz (1024 subcarriers) and 100 MHz (2048 subcarriers). F_SC = 48.828125 kHz.

• For coaxial cables, two baseband bandplans, 50 MHz (256 subcarriers) and 10 MHz (512 subcarriers), and two RF bandplans with bandwidth of 50 MHz (256 subcarriers) and 100 MHz (512 subcarriers). F_SC = 195.3125 kHz.

G.hn specifies a transmit PSD mask that the transmitter should apply to the signal before transmission. This mask is composed of a limit PSD mask defined in G.hn for each particular medium, notching of international amateur radio bands and other services and any other notching or mask shaping dictated by local regulations.

12.2.4.2 Frames Transmitted and Received by the G.hn Transceiver

The G.hn transceiver, acting in the role of either an end point node or a DM, is transmitting and receiving frames (‘PHY frames’) with a general structure which consists of a preamble, header and payload. This structure is illustrated in Figure 12.2.

The preamble is a training sequence used by the receiver for detecting the transmitted PHY frame, training the receiver’s AGC, acquiring frequency and time synchronisation and performing initial channel estimates.

The PHY frame header (PFH) is a field of 168 information bits carrying control information, such as the type of the frame and its length; parameters of the PHY related to the payload, such as the length of the guard interval, identification of the bit-loading vector and parameters of the forward error correction (FEC); and also some control information related to the DLL sub-layer mechanisms. In order to guarantee robust transmission of the header, it is transmitted usually over a single OFDM symbol with a FEC code rate of 1/2, bit loading of 2, that is, a constellation of quadrature phase shift keying (QPSK) over all of the active subcarriers (ASCs) and a strong repetition.

G.hn specifies several PHY frame types used for different purposes. Some of the specified frame types are listed in Table 12.1. As mentioned in this table, some of the frame types carry information only in the header and do not include a payload.

Some of the mechanisms using the previous frame types (e.g. retransmissions and more) are briefly reviewed in Section 12.2.7.

FIGURE 12.2
Format of the G.hn’s PHY frame.

TABLE 12.1

PHY Frame Types

Frame Type	Description	Header	Payload
MSG	The basic PHY frame carries user data or management data or both.	√	√
MAP/RMAP	A frame transmitted by the DM, carrying the MAP (scheduling information of the MAC cycle) or relayed MAP.	√	√
ACK	An acknowledgment frame. The relevant ARQ control data are communicated in the header.	√	none
PROBE	A frame carrying probe symbols (for channel and noise estimation) in its payload.	√	√

Source: ITU-T. 2010. G.9961, Unified high-speed wire-line based home networking transceivers – Data link layer specification. With permission.

Note: Few additional PHY frame types are specified in the G.hn specifications.

The payload, which is transmitted over multiple OFDM symbols, delivers data which encapsulate higher-layer information. This encapsulation is described in Section 12.2.4.4. The payload’s data are scrambled and coded using a low-density parity check (LDPC) FEC code with a flexible code rate, supporting code rates of 1/2, 2/3, 5/6, 16/18 and 20/21 and two possible information block sizes, 120 and 540 bytes. G.hn also specifies flexible loading of bits onto the OFDM symbols. Each subcarrier of a payload OFDM symbol can be loaded with a different number of bits, ranging from 1 to 12 bits (the loading is fixed per subcarrier index along the time axis, i.e. over all OFDM symbols of the payload).

12.2.4.3 Protocol Reference Model of the G.hn Transceiver

The protocol reference model of the G.hn transceiver is presented in Figure 12.3. The G.hn standard specifies the PHY and the DLL, that is, layers 1 and 2 of the open systems interconnection (OSI) model.

The DLL is composed of the following sub-layers:

• The application protocol convergence (APC) sub-layer provides an interface with the application entity (AE), which operates with an application-specific protocol, such as Ethernet. The APC also classifies the incoming data into flows and may provide data rate adaptation between the AE and the home network transceiver in the receive direction.

• The logical link control (LLC) sub-layer is responsible for encrypting the transmitted data and handling the security protocols, managing the data path of the retransmissions mechanism, supporting the relaying functionality, managing connections of the node inside the domain and facilitating quality of service (QoS) constraints for the connections.

• The MAC sub-layer controls access of the node to the medium using the various specified medium access protocols.

The PHY, as described in the G.hn standard, is also composed of several sub-layers; however, for simplicity reasons, the description hereafter treats the PHY as a single entity.

FIGURE 12.3
Protocol reference model of the G.hn home network transceiver. (Based on figure 5-11 from ITU-T. 2011. G.9960, Unified high-speed wireline-based home networking transceivers – System architecture and physical layer specification. With permission.)

The PHY encapsulates the data units obtained from the MAC, into PHY frames, adding a preamble (for various synchronisation and estimation purposes) and a PFH (containing control parameters). The PHY provides forward error correction (FEC) of the PHY frame content (header and payload) and loads the coded bits onto the subcarriers of OFDM symbols, according to bit allocation tables (BATs). The front-end operations in the PHY include the OFDM modulator, the inverse discrete Fourier transform (IDFT), cyclic prefix, the transmit filters (in order to meet regulations) and the AFE. Further description appears in the following sections.

The reference model of Figure 12.3 also identifies the interfaces of the G.hn transceiver. The external interfaces are the A-interface, the interface to the AE, which is user/application dependent (e.g. Ethernet, IP); the medium-dependent interface (MDI), which is the physical interface to the medium (i.e. power lines, phone lines and coaxial cables); and the internal interface between the DLL and PHY (the physical medium-independent interface [PMI]). The layers above the DLL (above the A-interface) are beyond the scope of the G.hn standard.

12.2.4.4 Data-Plane Processing in the DLL

The overall functional model of the DLL is presented in Figure 12.4.

This section provides a brief overview of the processing of data within the DLL. In addition to this data-plane processing functionality, the DLL provides control-plane functionalities. The interested reader is referred to [1] for further information on these functionalities.

In the transmit direction, application data primitive (ADP) sets enter the DLL from the AE across the A-interface. Every incoming ADP meets a format defined by a particular application protocol (e.g. Ethernet frames). Each incoming ADP is converted by the APC sublayer into APC protocol data units (APDUs), which include all parts of the ADP set intended for communication to the destination node(s). The APDUs are transferred to the LLC sublayer via the x₁-interface. Processing of the data within the G.hn transceiver from this point onward is described in Figure 12.5. In addition to the incoming APDUs, the LLC sub-layer receives management data primitives from the DLL management entity intended for LLC control frames, which are assembled into link control data units (LCDUs).

FIGURE 12.4
Functional model of the DLL and partitioning into sub-layers. (Based on figure 8-1 from ITU-T. 2010. G.9961, Unified high-speed wire-line based home networking transceivers – Data link layer specification. With permission.)

FIGURE 12.5
Processing of data by the G.hn transmitter.

In the LLC, APDUs and LCDUs are converted into LLC frames, by adding an LLC frame header (LFH), and may be encrypted using assigned encryption keys. In this case, an additional header, the CCM encryption protocol (CCMP) header (CCM is the counter with cipher block chaining message authentication code), and footer (the message integrity code [MIC]) information are added. The LLC frame is the basic unit which is subject to the relaying functionality which the LLC manages (G.hn facilitates relaying of both data and management information in layer 2). Several LLC frames are concatenated to form an LLC frame block (this block will eventually fit into the payload part of a single PHY frame).

The LLC frame block is then segmented to segments of equal size (at a previous stage padding, bits are added to the LLC frame block so that its length is an integer multiple of a segment size). Each segment is transformed into an LLC protocol data unit (LPDU) by adding an LPDU header (LPH) and cyclic redundancy code (CRC). The LPDUs are of fixed size of either 540 or 120 bytes. These segments are the basic data unit used for the retransmission mechanism which is controlled by the LLC layer and are also the basic units which in the PHY will be subject to FEC encoding.

The LPDUs are transferred to the MAC sub-layer via the x₂-interface. The only data-plane processing performed in the MAC is assembling of a MAC protocol data unit (MPDU) out of the incoming LPDUs. This MPDU is transferred to the PHY via the PMI interface (this MPDU is mapped in the PHY into the payload of a single PHY frame).

12.2.4.5 PHY of the G.hn Transceiver

The functional model of the PHY of the G.hn transmitter is presented in Figure 12.6 (the G.hn standard, as any other standard, specifies the transmitter. The receiver is vendor discretionary).

The following sections describe the transmission flow and the operation of the different PHY building blocks.

12.2.4.5.1 Data Scrambling (for the Header and Payload)

The inputs to the PHY at the PMI reference point are MPDUs coming from the DLL. Each MPDU is mapped to the payload of a single PHY frame. PFH bits are assembled from control information conveyed by the transceiver’s management entity (generally, the header carries 168 information bits. There are few exceptions in which the header uses twice this size) and prepended to the payload. This block of bits composed of the header and payload are scrambled (Xor-ed) with a pseudorandom sequence generated by a specific linear feedback shift register (LFSR).

12.2.4.5.2 Header and Payload FEC Encoding

After scrambling, both the header and the payload are encoded using a FEC code. The G.hn FEC is using a systematic quasi-cyclic LDPC block code (QC LDPC BC). In the process of selecting the coding scheme for G.hn, the LDPC code was evaluated along with a duo-binary cyclic turbo code (DB-CTC). While CTC offers good performance at high block error rates (BLERs), for example, BLERs of 10⁻²–10⁻³. which are typical in harsh environments such as power lines, it suffers from a known phenomenon of an error floor in low BLER regions, for example, BLERs of 10⁻⁶–10⁻⁸ which are typical to very benign media-like coax. LDPC, on the other hand, was shown [5] to perform well in a wide range of BLERs (LDPC shows substantial gains over DB-CTC at low BLERs and offers the same or better coding gains at low BLERs), thus proven to be adequate to G.hn intended for multiple media and supporting a wide variety of applications. In addition, LDPC yields itself to very efficient implementations at high rates and is preferred over CTC in many of the recent high-speed communication standards, such as WiFi (IEEE 802.11n and IEEE 802.11ac), DVB-S2/DVB-T2/DVB-C2 (digital video broadcasting, 2nd generation) and 10GBase-TEthernet (IEEE 802.3an).

FIGURE 12.6
Functional model of the PHY of a G.hn transceiver.

FIGURE 12.7
FEC encoder. (Based on figure 7-7 from ITU-T. 2011. G.9960, Unified high-speed wireline-based home networking transceivers – System architecture and physical layer specification. With permission.)

The structure of the FEC encoder, composed of the LDPC encoder and a puncturing mechanism, is illustrated in Figure 12.7.

In Figure 12.7, K is the size of information block, N_M is the size of coded block (before puncturing), N_M − K is the number of parity check bits and N_FEC ≤ N_M is the size of the FEC codeword [after puncturing]. The rates related to the coding scheme are R_M = K/N_M (the mother code rate [before puncturing]) and R = K/N_FEC (the code rate [after puncturing]).

For the header encoding, the information block size is 168 bits. Header encoding is done using a single mother code with rate R_M = 1/2 (corresponding to a mother code matrix, denoted (1/2)_H).

For the payload encoding, two possible information block sizes are specified: 960 bits (referred to as ‘short’ blocks) or 4320 bits (referred to as ‘long’ blocks). The G.hn payload encoding scheme specifies five code rates 1/2, 2/3, 5/6, 16/18 and 20/21. The encoder is based on mother codes with rates R_M = 1/2, R_M = 2/3 and R_M = 5/6 for each of the information block sizes (corresponding to mother code matrices denoted (1/2)_S, (1/2)_L, (2/3)_S, (2/3)_L, (5/6)_S and (5/6)_L, where the matrices with subscript S are used for coding the short blocks and the ones with subscript L are used for the long blocks). From these mother codes, codes with higher code rates are obtained through puncturing, that is, codes with rates 16/18 and 20/21. The codeword at the output of the puncturing block is of size N_FEC ≤ N_M. Table 12.2 summarises all of the coding options.

12.2.4.5.3 Header and Payload Repetition Encoding

In order to improve robustness of transmissions, G.hn specifies a robust communication mode (RCM) which is a mode in which encoded data blocks are repeated N_REP times. There are two variants for this mode of operation, one specified for the header and for the payload.

The header processing always includes repetition. The coded header block, of size 336 bits (168 bits LDPC coded with rate 1/2), is repeated N_REP times:

$N_{R E P} = ceiling (k_{H} / N_{F E C}),$ $N_{R E P} = ceiling (k_{H} / N_{F E C}),$

where k_H is the number of bits to be loaded onto the OFDM symbol carrying the header (equal to 2 bits per subcarrier × the number of supported subcarriers [SSCs]) and N_FEC = 336 bits. The N_REP copies are concatenated, where the bits of each copy are cyclically shifted by 2 bits within the copy. The bits of this concatenated block are loaded onto subcarriers in the PMD sub-layer.

For the payload, RCM may be applied in MSG frames following a decision of either the receiver or the transmitter: The transmitter may choose to use RCM immediately after establishing a connection with a receiver and prior to having runtime BATs established; the receiver may choose to request the transmitter to use RCM if channel conditions are very bad. The number of repetitions is determined by the transmitter or receiver based on the needed robustness. G.hn supports payload repetition factors of N_REP = 2, 3, 4, 6, 8. Without getting into the finer details of the repetition mechanism, it can be said that this mechanism spreads and shuffles the copies of each FEC codeword in both frequency and time (i.e. over multiple OFDM symbols), depending on N_REP, N_FEC and K_P, which is the number of bits to be loaded onto a payload OFDM symbol (equal to 2 bits per subcarrier × the number of SSCs). This is done to optimise the diversity gained by the repetition.

TABLE 12.2

FEC Encoding Parameters

	Code Rate (R)	Information Block Size, K (Bits)	Mother Code Matrix	FEC Codeword Size, N_FEC (Bits)
For header	1/2	PHY_H = 168	(1/2)_H	336
For payload	1/2	960	(1/2)_S	1920
	1/2	4320	(1/2)_L	8640
	2/3	960	(2/3)_S	1440
	2/3	4320	(2/3)_L	6480
	5/6	960	(5/6)_S	1152
	5/6	4320	(5/6)_L	5184
	16/18	960	(5/6)_S	1080
	16/18	4320	(5/6)_L	4860
	20/21	960	(5/6)_S	1008
	20/21	4320	(5/6)_L	4536

Source: Based on table 7-56 from ITU-T. 2011. G.9960, Unified high-speed wireline-based home networking transceivers – System architecture and physical layer specification. With permission.

12.2.4.5.2.4 Tone Mapping and the Bit Allocation Table

The tone mapper divides the incoming encoded header and payload blocks into groups of bits, according to a BAT and subcarrier grouping being used, and associates each group of bits with specific subcarriers onto which these groups shall be loaded. The BAT is a vector associating each subcarrier index along the frequency axis with the number of bits to be loaded on it. A BAT is identified with an identifier called BAT_ID that is indicated in the PFH of each frame transmission.

Two types of BATs are defined:

1. Predefined BATs: A set of fixed mappings between subcarrier indices and bit loadings. These mappings are specifying fixed loadings of 1 or 2 bits over all of the (non-masked) subcarriers. These mappings are associated with fixed BAT_IDs.

2. Runtime BATs: Mappings that are established for a specific link between a transmitter (source node) and receiver (a destination node), after negotiation and agreement between the two. This negotiation process is part of the ‘channel estimation’ protocol during which a BAT_ID is dynamically associated to specific runtime BATs.

The PFH is defined with a fixed bit loading of 2 bits on each of the non-masked subcarriers (non-MSCs). The payload of the MSG frame can use either the predefined or runtime BATs.

Several different BATs (and BAT_IDs) may be established for a specific link between transmitter and receiver. In addition, BATs may be valid for only a specific portion of the MAC cycle. For example, for a network operating over power lines, in which the MAC cycle is equal to two alternating current (AC) cycles, a receiver may divide the AC cycle into intervals and associate each interval of the AC cycle with a different BAT (and BAT_ID). This can be used to cope with the typical cyclic variation of the channel impulse response, noise and interference of the power lines media, synchronised with the AC (mains) cycle.

The establishment of runtime BATs usually involves communicating the explicit BAT (an ordered vector of bit loadings) from the receiver to the transmitter which consumes time on the media. In addition, both the receiver and transmitter need to save the BATs associated with each of their links. In order to reduce the overhead incurred by communication of the BATs over the media and reduce the transmitter and receiver memory requirements, BAT grouping may be used. If grouping is used, all of the subsequent subcarriers of the same group, with G subcarriers, shall use the same bit loading. A G.hn node is capable of supporting grouping of any runtime BAT using grouping of G = 1 (no grouping), 2, 4, 8 and 16 subcarriers.

The tone mapper takes into consideration the following types of subcarriers for the purpose of tone mapping:

1. Masked subcarriers (MSCs): Subcarriers on which transmission is not allowed. These subcarriers are not loaded with bits.

2. Supported subcarriers (SSCs): Subcarriers on which transmission is allowed under restrictions of the relevant PSD mask. The number of SSCs is #SSC = N − #MSC. The following types of SSC are defined:

a. Active subcarriers (ASCs): Subcarriers that have loaded bits (b ≥ 1) for data transmission. ASCs are subject to constellation point mapping, constellation scaling and constellation scrambling.

b. Inactive subcarriers (ISCs): Subcarriers that do not have any data bits loaded (e.g. because the SNR is low). The number of ISCs is #ISC = #SSC − #ASC. These subcarriers are loaded with a pseudorandom sequence of constellation points, as described later on. ISCs can be used for measurement purposes.

12.2.4.5.5 Bit Generation and Loading for Inactive and Partially Loaded Subcarriers

There are two cases in which subcarriers of the payload symbols of a MSG frame are loaded or partially loaded with a pseudorandom sequence of bits generated by an LFSR generator, rather than with encoded data bits:

• ISCs with zero data bit loading (b = 0). This is usually the result of the receiver (which is usually the node calculating the BATs and communicating them to the transmitter) coming to the conclusion that the SNR on this subcarrier is too low. In this case two bits are taken from the LFSR and loaded on these subcarriers.

• In cases where the number of bits in the encoded payload is not enough to completely fill all subcarriers of the last OFDM symbol in the PHY frame, these last subcarriers will be loaded with bits from the mentioned LFSR. There may be two types of such subcarriers: One subcarrier may be partially loaded with the last few bits from the encoded payload and the rest are taken from the LFSR (this subcarrier is actually an ASC). If there are more subcarriers following this subcarrier in the OFDM symbol, they will be loaded with bits from the LFSR (these last subcarriers are categorised as ISCs). The number of bits loaded from the LFSR on these subcarriers is according to the BAT.

The mentioned LFSR is also used to load the payload symbols of probe frames, also called ‘probe symbols’. Both types of symbols are defined as composed of only ISCs. These subcarriers are loaded with 2 bits per subcarrier taken from the LFSR. The probe symbols may be used by receivers for channel and noise estimation purposes.

12.2.4.5.2.6 Constellation Mapping and Scaling

Constellation mapping associates every group of b bits, ${d_{b - 1}, d_{b - 2}, \dots, d_{0}}$ ${d_{b - 1}, d_{b - 2}, \dots, d_{0}}$ , loaded onto a subcarrier, with the values of I (in-phase component) and Q (quadrature-phase component) of a constellation diagram.

G.hn specifies constellations with loading of up to 12 bits per subcarrier, as shown in Figure 12.8. All of the even-ordered constellations, that is, loading of 2, 4, 6, 8, 10 and 12 bits per subcarrier, are mandatory for both the transmitter and receiver sides. Theses constellations are square-shaped QAM constellations.

The support of all odd-ordered constellations, that is, loading of 1, 3, 5, 7, 9 and 11 bits per subcarrier, is mandatory for the transmitter. For the receiver, the support of loading of 1 and 3 bits is mandatory, and all other bit loadings with b ≥ 5 are optional. The constellations with b ≥ 5 are cross-shaped constellations.

FIGURE 12.8
Constellation mapping (b = 1, 2, 3, …, 12).

Mapping of bits into the constellation points is specified in the G.hn standard and basically follows the known Gray-mapping rules (for all even-ordered constellations and most of the odd-ordered constellations).

Each constellation point (I, Q), corresponding to the complex value I + jQ at the output of the constellation mapper, shall be scaled by a power-normalisation factor χ(b):

$Z = χ (b) \times (I + j Q) .$ $Z = χ (b) \times (I + j Q) .$

The normalisation factor, χ(b), for a subcarrier with b bit loading depends only on the value of b. This factor is calculated so that the values (I, Q) for each constellation point (of each subcarrier) are scaled such that all constellations, regardless of their size, have the same normalised average power equal to 1.

12.2.4.5.7 Constellation Scrambling

An OFDM signal is the weighted sum of N independent narrowband signals (subcarriers). At some time instances, the phases of these independent signals might constructively combine, resulting in a large sum value, while at other times this sum may be small (due to destructive combining). This means that the peak value of the OFDM signal is substantially larger than the average value. This high peak-to-average power ratio (PAPR) property is one of the known issues with OFDM.

The phase of constellation points generated by the constellation mapper and scaler is phase shifted (rotated) in accordance with a pseudorandom sequence generated by an LFSR generator. This operation, applied to the subcarriers of the entire frame (including the preamble), reduces the probability of constrictive or destructive combining of the signals constituting the OFDM symbol, thus resulting in lower PAPR of the transmitted OFDM signal. The LFSR is advanced by 2 bits on each subcarrier, and these two output bits are used to determine the phase from the range ${0, π / 2, π, 3π / 2}$ ${0, π / 2, π, 3π / 2}$ . This operation is described as

$Z_{i, l} = Z_{i, l}^{0} \cdot \exp (j θ) for l =0, \dots {,M}_{F} - 1, i = 0, \dots, N - 1,$ $Z_{i, l} = Z_{i, l}^{0} \cdot \exp (j θ) for l =0, \dots {,M}_{F} - 1, i = 0, \dots, N - 1,$

where

$Z_{i, l}^{0}$ $Z_{i, l}^{0}$ is the originally mapped constellation point

l is the index of the OFDM symbol within the current frame (M_F denotes the total number of OFDM symbols in the current frame)

i is the index of the subcarrier within the OFDM symbol

θ is the rotation phase

Z_i,_l is the output of the constellation scrambler (which is fed as input to the IDFT)

12.2.4.5.8 Preamble Generation

The preamble is composed of up to three sections. Each section I comprises N_I repetitions of an OFDM symbol (‘mini-symbol’) S_I employing subcarrier spacing k_I × F_SC, where F_SC denotes the subcarrier spacing of the payload OFDM symbols. The third section is only included for the coax media case (and not for power lines or phone lines). The values of k_I can be selected from the set 1, 2, 4 or 8. The subcarriers of section I are spaced such that one subcarrier is included for every k_I subcarriers used for the payload OFDM symbol. The subcarrier spacing of the second section is equal to the subcarrier spacing of the first section (k₂ = k₁). The symbols of the second section are an inverted time-domain waveform of the first section (S₂ = –S₁). This forms a reference point to detect the start of the received frame Each preamble section is windowed in order to comply with the PSD mask, as illustrated in Figure 12.9.

FIGURE 12.9
Structure of the G.hn preamble. (Based on figure 7-25 from ITU-T. 2011. G.9960, Unified high-speed wireline-based home networking transceivers – System architecture and physical layer specification. With permission.).

The non-MSCs of the preamble have a bit sequence of all ones mapped onto them using 1-bit constellations. Following this mapping, constellation phase rotation is applied to the preambles subcarriers using the constellation scrambler described in Section 12.2.4.5.7. The LFSR generator of the constellation scrambler is initialised at the beginning of each one of the used preamble sections to a seed that is section and medium dependent.

As an example, the preamble used for the power lines media comprises only two sections. The first section is composed of 7 mini-symbols and the 2nd of 2 mini-symbols. The two sections use k₁ = k₂ = 8.

12.2.4.5.9 OFDM Modulation

The functional diagram of OFDM modulator is presented in Figure 12.10.

The incoming signal to the modulator is a set of N complex values z_i,l generated either by the constellation encoder (for symbols of the header and the payload) or by the preamble generator (for symbols of the preamble). The IDFT converts the stream of N complex numbers z_i,l into a stream of N complex time-domain samples x_n,l:

$x_{n, l} = \sum_{i = 0}^{N - 1} \exp (j \cdot 2 π \cdot i \frac{n}{N}) \cdot z_{i, l} for n = 0 to N - 1, l = 0 to M_{F} - 1.$ $x_{n, l} = \sum_{i = 0}^{N - 1} \exp (j \cdot 2 π \cdot i \frac{n}{N}) \cdot z_{i, l} for n = 0 to N - 1, l = 0 to M_{F} - 1.$

Following the IDFT, a cyclic prefix is added by prepending the last N_CP(l) samples of the IDFT output to its output N samples. This guard interval is intended to protect against inter-symbol interference (ISI). The lth OFDM symbol after cyclic prefix addition consists of $N_{W} (l) = N + N_{C P} (l)$ $N_{W} (l) = N + N_{C P} (l)$ samples and is described by the following equation:

FIGURE 12.10
Functional model of the OFDM modulator. (Based on figure 7-23 from ITU-T. 2011. G.9960, Unified highspeed wireline-based home networking transceivers – System architecture and physical layer specification. With permission.)

FIGURE 12.11
Structure of an OFDM symbol with cyclic extension and overlapped windowing. (Based on figure 7-24 from ITU-T. 2011. G.9960, Unified high-speed wireline-based home networking transceivers – System architecture and physical layer specification. With permission.)

$υ_{n, l} = x_{n - N_{C P} (l), l} = \sum_{i = 0}^{N - 1} z_{i, l} \times \exp (j \cdot 2 π \cdot i \frac{n - N_{C P} (l)}{N}) for n =0 to N_{W} (l) - 1= N + N_{C P} (l) - 1 .$ $υ_{n, l} = x_{n - N_{C P} (l), l} = \sum_{i = 0}^{N - 1} z_{i, l} \times \exp (j \cdot 2 π \cdot i \frac{n - N_{C P} (l)}{N}) for n =0 to N_{W} (l) - 1= N + N_{C P} (l) - 1 .$

NOTE: The cyclic shift operation does not apply for the preamble.

Following cyclic prefix addition, the time-domain samples are subject to windowing. Windowing shapes the envelope of the transmitted signal to facilitate PSD shaping: it allows sharp PSD roll-offs used to create deep spectral notches and reduction of the out-of-band PSD. The windowing for all OFDM symbols excluding the preamble is done on the first β samples of the cyclic prefix and last β samples of the IDFT output. To reduce the modulation overhead, the windowed samples of adjacent symbols overlap, as shown in Figure 12.11. The value of $N_{C P} (l) - β = N_{G I} (l)$ $N_{C P} (l) - β = N_{G I} (l)$ forms the guard interval. The duration of the lth OFDM symbol after overlap is thus $N_{S} (l) = N + N_{C P} (l) - β$ $N_{S} (l) = N + N_{C P} (l) - β$ . The windowing and the overlap and add operation on the preamble are done on each of the preamble sections separately as can be seen in Figure 12.9.

After applying the windowing and the overlap and add functions, the time-domain samples at the reference point u_n in Figure 12.10 comply with the following equation:

$u_{n} = u_{n}^{(p r)} + \sum_{l = 0}^{M_{F} - 1} w (n - M (l), l) \cdot υ_{n - M (l), l} for n =0 to M (M_{F} - 1) + N_{W} (M_{F} - 1) - 1,$ $u_{n} = u_{n}^{(p r)} + \sum_{l = 0}^{M_{F} - 1} w (n - M (l), l) \cdot υ_{n - M (l), l} for n =0 to M (M_{F} - 1) + N_{W} (M_{F} - 1) - 1,$

where

$u_{n}^{(p r)}$ $u_{n}^{(p r)}$ is the nth sample of the preamble (the signal $u_{n}^{(p r)}$ $u_{n}^{(p r)}$ already includes windowing as necessary)

w(n, l) is the windowing function and is vendor discretionary

M(l) is the index of the first sample of the lth symbol

The symbol rate f_OFDM (number of symbols per second) and symbol period T_OFDM for the given value of N_CP and β shall be computed, respectively, as

$f_{O F D M} = \frac{N \times F_{S C}}{N + N_{C P} - β} and T_{O F D M} = \frac{1}{f_{O F D M}} .$ $f_{O F D M} = \frac{N \times F_{S C}}{N + N_{C P} - β} and T_{O F D M} = \frac{1}{f_{O F D M}} .$

The number of IDFT samples, N, and the number of windowed samples, β, are constant over the frame. The value of N_CP(l) (and the duration of the pre-overlapped OFDM symbol N_w(l), accordingly) may change during the course of the frame, as follows:

• The header symbol and the first two symbols of the payload use a default value $N_{G I - H D} + β .$ $N_{G I - H D} + β .$

• All the rest of the payload symbols use a value of N_GI which may be different than the default value, selected from a valid range of values mentioned in Tables 12.3 through 12.5 and indicated in the header.

The frequency up-shift block from Figure 12.10 offsets the spectrum of the transmit signal, shifting it by F_US (the value of F_US for each bandplan is mentioned later on in Tables 12.3 through 12.5):

$s_{n} = u_{n / p} \times \exp (j \frac{2 π m n}{N p}) = R e (s_{n}) + j I m (s_{n}); for n = 0 to [M (M_{F} - 1) \times N_{W} (M_{F} - 1)] \times p - 1,$ $s_{n} = u_{n / p} \times \exp (j \frac{2 π m n}{N p}) = R e (s_{n}) + j I m (s_{n}); for n = 0 to [M (M_{F} - 1) \times N_{W} (M_{F} - 1)] \times p - 1,$

where u_n/p is u_n after interpolation with factor p. The interpolation factor p is vendor discretionary and is equal to or higher than 2 (the minimum value of p sufficient to avoid distortions depends on the ratio between the up-shift frequency F_US and the bandwidth of the transmit signal $BW = N^{*} F_{S C}$ $BW = N^{*} F_{S C}$ . It is assumed that an appropriate low-pass filter is included to reduce imaging).

For baseband bandplans, the output signal of the modulator is the real component of s_n:

$S_{o u t - B B} = R e (s_{n}) .$ $S_{o u t - B B} = R e (s_{n}) .$

For the RF bandplans (i.e. coax RF),the RF up-converter produces the following output signal:

$S_{o u t - R F} (t) = R e [s (t) \times \exp (j 2 π F_{U C} t)] = R e [s (t)] \times \cos (2 π F_{U C} t) - I m [s (t)] \times \sin (2 π F_{U C} t),$ $S_{o u t - R F} (t) = R e [s (t) \times \exp (j 2 π F_{U C} t)] = R e [s (t)] \times \cos (2 π F_{U C} t) - I m [s (t)] \times \sin (2 π F_{U C} t),$

TABLE 12.3

OFDM Control Parameters for Power Lines Baseband

	25 MHz (Notes 1, 2)	50 MHz (Notes 1, 2)	100 MHz (Notes 1, 2)
N	1024	2048	4096
F_SC	24.4140625 kHz	24.4140625 kHz	24.4140625 kHz
N_GI	N/32 × k, k = 1,…,8	N/32 × k, k = 1,…,8	N/32 × k, k = 1,…,8
N_GI–DF	N/4	N/4	N/4
β	N/8	N/8	N/8
F_US	12.5 MHz	25 MHz	50 MHz

Source: Based on table 6-4 from ITU-T. 2010. G.9964, Unified high-speed wireline-based home networking transceivers – Power spectral density specification. With permission.

Note 1: The range of subcarrier frequencies is between 0 and 2 × F_US MHz.

Note 2: The 25, 50 and 100 MHz bandplans may be used by nodes operating in the same power line domain.

TABLE 12.4

OFDM Control Parameters for Phone Lines (Baseband)

	50 MHz (Notes 1, 2)	100 MHz (Notes 1, 2)
N	1024	2048
F_SC	48.828125 kHz	48.828125 kHz
N_GI	N/32 × k, k = 1,…,8	N/32 × k, k = 1,…,8
N_GI–DF	N/4	N/4
β	N/32	N/32
F_US	25 MHz	50 MHz

Source: Based on table 6-1 from ITU-T. 2010. G.9964, Unified high-speed wireline-based home networking transceivers – Power spectral density specification. With permission.

Note 1: The range of subcarrier frequencies is between 0 and 2 × F_US MHz.

Note 2: The 50 and 100 MHz bandplans may be used by nodes operating in the same telephone-line domain.

TABLE 12.5

OFDM Control Parameters for Coax Cables

	Coax Baseband		Coax RF
	50 MHz (Notes 1, 3)	100 MHz (Notes 1, 3)	50 MHz (Notes 2, 3)	100 MHz (Notes 2, 3)
N	256	512	256	512
F_SC	195.3125 kHz	195.3125 kHz	195.3125 kHz	195.3125 kHz
N_GI	N/32 × k, k = 1,…,8	N/32 × k, k = 1,…,8	N/32 × k, k = 1,…,8	N/32 × k, k = 1,…,8
N_GI–DF	N/4	N/4	N/4	N/4
β	N/32	N/32	N/32	N/32
F_US	25 MHz	50 MHz	25 MHz	50 MHz

Source: Based on table 6-6 from ITU-T. 2010. G.9964, Unified high-speed wireline-based home networking transceivers – Power spectral density specification With permission.

Note 1: The range of subcarrier frequencies is between 0 and 2 × F_US MHz.

Note 2: The range of subcarrier frequencies is between F_UC and F_UC + 2 × F_US MHz.

Note 3: The 50 and 100 MHz baseband bandplans may be used by nodes operating in the same coax baseband domain. The same principle applies to 50 and 100 MHz bandplans defined for the coax RF domain.

where F_UC is the frequency shift introduced by the RF modulator. After RF up-conversion, the centre frequency around which the spectrum of the transmit OFDM signal will be placed is $F_{C} = F_{U C} + F_{U S} .$ $F_{C} = F_{U C} + F_{U S} .$ .

The OFDM modulator, as illustrated in Figure 12.10, is described in the G.hn standard in a parameterised way which is media-independent. For each media (power lines, phone lines and coax), a different set of parameters, optimised for the specific media characteristics, is used, as given in Tables 12.3 through 12.5.

Oksman and Galli [5] analysed the OFDM parameters needed for the different wired media types supported by G.hn (power lines, phone lines and coax cables). The reported findings include statistics (scatter plots and trend lines) of the root mean square delay spread (RMS-DS) versus the channel gain for the supported wire types. The RMS-DS is a key metric for optimising the cyclic prefix length (the cyclic prefix length should cover the maximal delay spread to avoid ISI) and the subcarrier spacing (the subcarrier spacing should be smaller than the coherence bandwidth of the channel, where the coherence bandwidth is proportional to the inverse of the maximal delay spread of the channel). These statistics show that the different media have distinct RMS-DS and channel gain characteristics, where the RMS-DSs of the three supported mediums are multiples of each other by a factor that is very close to a power-of-two (the 99% worst case RMS-DS of these media was found to be 1.75 μs for power lines, 0.39 μs for phone lines and 46 ns for coax). This leads to a conclusion that a power-of-two scalable OFDM solution is appropriate for all of the three types of wiring and allows one to calculate the OFDM parameters per each media. Practically the number of subcarriers is chosen to be higher than the ‘theoretical’ calculation for higher transmission efficiency, as long as the OFDM symbol length is not too long (so that the channel does not substantially change during a symbol) and if allowed by computational complexity and memory constraints.

12.2.4.5.10 Transmit PSD Mask and AFE

The signal transmitted by a G.hn transmitter is subject to a transmit PSD mask. The transmit PSD mask is composed of several elements, such as a limit PSD mask, a mechanism to digitally notch subcarriers and a mechanism for PSD shaping. The limit PSD mask is an upper bound on the allowed PSD and takes into account currently known regulation restrictions. As an example, Figure 12.12 shows the G.hn limit PSD specified for power lines.

The notching mechanism allows digital masking of subcarriers in bands that are not allowed for transmissions (such as bands allocated to amateur radio transmission, radio broadcasts and other radio services). The existence of these notches is either fixed or dynamically published by the DM (in the MAP) to all nodes in the domain. A G.hn node (transmitter) does not load any bits on these MSCs. Another mechanism allows the DM to publish PSD shaping of the mask in regions where stricter regulations exists compared to the limit PSD mask.

FIGURE 12.12
The limit PSD mask for transmissions over power lines for the 25, 50 and 100 MHz bandplans (notches not shown). (Based on figure 6-2 from ITU-T. 2010. G.9964, Unified high-speed wireline-based home networking transceivers – Power spectral density specification. With permission.)

The AFE of the transceiver includes the D/A and A/D converters, analogue filters and the (medium-dependent) line drivers. All of these are vendor discretionary.

12.2.5 G.hn’s Media Access

The access of nodes in a domain to the medium, that is, MAC in G.hn is managed by the DM and is synchronised with a cycle called the MAC cycle. This MAC cycle can be synchronised to an external source, and in particular for communication over power lines, the MAC cycle is defined to be synchronised to the mains (AC) cycle, and its length is fixed and equal to 2 AC cycles. This is done to assist in coping with the periodically time-varying nature of the power line channel and noise, which is the result of the power lines topology and electrical devices and appliances connected to the power outlets.

The MAC cycle is divided into time intervals which are assigned as TxOPs for different nodes or groups of nodes in the domain (Figure 12.13).

In each MAC cycle, at least one TxOP is assigned for the DM itself for transmission of the medium access plan (MAP). Other TxOPs are assigned by the DM to nodes (or groups of nodes) for transmission of data for various applications. Several types of TxOPs are specified, in which different MAC rules are defined, as explained later on.

Nodes in the domain synchronise with the MAC cycle, decode the MAP and transmit only during TxOPs assigned to them by the DM (transmission in each TxOP is according to the specific MAC rules of that TxOP). Frames transmitted inside a TxOP are separated by inter-frame gaps (IFGs). During IFGs the medium is idle.

The DM is responsible for setting up the scheduling in the domain, that is, the length of the MAC cycle (which is fixed for the power lines media, but not for other media types) and the number, timing and parameters of TxOPs in the MAC cycle. This scheduling is set by the DM based on requests for bandwidth from the nodes and may change from one MAC cycle to the other in order to accommodate possible variations of the load in the network, number of registered nodes, changes in the channel conditions, etc.

12.2.5.1 Media Access Plan

The media access plan (MAP) transmitted in MAC cycle n contains scheduling information on MAC cycle n + 1. The MAP includes the following scheduling information: identification of the boundaries of the MAC cycle, boundaries and content of each one of the TxOPs (the MAC used in the TxOP and its parameters, assignment of nodes or priorities to TxOPs or time slots [TSs] within a TxOP and more) and global information needed for the operation of the domain such as regional PSD notches and masks used in the domain. This MAP is broadcasted in the domain by the DM via a MAP PHY frame that is also retransmitted by nodes assigned to be MAP relays, in order to guarantee that the MAP is received by all nodes in the domain.

FIGURE 12.13
G.hn’s MAP-controlled MAC-cycle-synchronised medium access.

12.2.5.2 Transmission Opportunities and Time Slots

G.hn specifies several MAC methods with different rules by defining several TxOP types. Each TxOP type specifies a specific MAC method. This was done in order to address different application demands and network conditions (network load, number of nodes, channel characteristics, etc). The DM determines which of these MAC methods to use. It may choose to use a single MAC method or a mix of these methods along the MAC cycle. All G.hn end point nodes mandatorily support all of the MAC methods (to guarantee interoperability). The different TxOP types can be classified into two categories:

1. Contention-free TxOP (CFTxOP)

2. Shared TxOP (STxOP)

The DM partitions the MAC cycle into CFTxOPs and STxOPs in accordance with service requirements of the domain’s nodes and other scheduling issues.

12.2.5.2.1 Contention-Free TxOP

This transmission opportunity is allocated by the DM to a single node, and therefore, transmission in this TxOP is contention-free (i.e. transmissions without collisions). One example for usage of this MAC scheme is the dedicated CFTxOP allocated by the DM in each one of the MAC cycles, for transmission of the MAP itself. This TxOP may also be used for guarantying QoS for certain applications.

12.2.5.2.2 Shared TxOP

An STxOP is divided into a grid of one or more TSs where each TS represents an opportunity to start transmitting for the node or a group of nodes assigned to this TS. The grid starts at the beginning of an STxOP. If a node assigned to the TS gains access to the media, the grid is frozen until the end of the transmission (the TS is virtually expanded). The grid timing is reset after the end of each transmission. A node assigned to the TS may either use the opportunity to start transmitting during the TS or pass on the opportunity to transmit. Transmission rules within each TS depend on the type of the TS. If the node passes on the opportunity, it waits until the next opportunity to transmit in a subsequent TS assigned for this node. The duration of a TS is medium-dependent (e.g. 35.84 μs for power lines). An STxOP can contain the following types of TSs (these are actually two different variants of MAC schemes):

1. Contention-free TS (CFTS)

2. Contention-based TS (CBTS)

An STxOP can be composed of only CFTSs, only CBTSs or both CFTSs and CBTSs.

A CFTS is a TS assigned for a single node. Other nodes monitor the line (virtual carrier sensing) in order to track the TS grid and be synchronised with the TSs assigned for them for transmission. In this sense, although the STxOP as a whole is shared, the TS MAC itself exhibits a managed carrier-sense, contention-free (i.e. collision avoidance) MAC scheme (i.e. CSMA/CA). This scheme is beneficial for services with flexible bandwidth where QoS is an issue (e.g. VoIP, games, interactive video).

A CBTS is a TS assigned to a group of nodes or to transmissions with a predefined priority or higher (meaning that all nodes which have data of a certain priority or higher can contend for transmission on the line) and therefore exhibits a contention-based MAC (i.e. collisions can occur). This scheme is beneficial for best effort services. There are multiple flavours of CBTS MAC schemes. In the most complex scheme, transmission in a TS is performed in the following way: The node wanting to contend for access to the media transmits an INUSE signal, signalling that it has data to transmit, followed by priority resolution signals (PRSs) that indicates the priority of the frame it intends to send. The PRS signalling is built in a way that allows a node to first monitor to see if other nodes have data of higher priority to send before it signals the priority of its planned transmissions. The PRS signalling selects nodes with frames of highest priority: only these nodes are allowed to contend, while all others back off to the next contention period. The probability of collision between the selected nodes is reduced by a random pick of the particular transmission slot inside a contention window. From the beginning of the window, all selected nodes monitor the medium (by carrier sensing). If the medium is inactive at the slot picked by the node, the node transmits its frame; otherwise, it backs off to the next contention period.

12.2.6 Establishing a G.hn Domain and Communication between Nodes of the Domain

Following is a description of how a G.hn domain is established and how nodes in the domain establish communication between each other. Steps 1 through 3 are used to establish a G.hn domain:

1. Forming a domain (DM selection): A domain is started by connecting (and powering up) one or several nodes to the media. These nodes will first look for an existing domain (by trying to detect MAPs from an existing DM) and in the lack of such will undergo a process of selecting a single DM among themselves. The user (or installer of the network) may configure one node to be the DM or it may be automatically selected to be a DM following certain criteria (e.g. if it has the highest visibility of other nodes). Once a node is selected as a DM, it will select a unique domain ID and start transmitting the MAPs conveying the scheduling of the MAC cycle.

2. Admitting (registration) new nodes into the domain: End point nodes wishing to join a domain first detect and decode the MAPs and then undergo a process of registration to the domain, during which they convey their capabilities to the DM and receive a unique device ID and other information unique to the domain. After the registration is confirmed, the newly registered node may start communicating with other nodes in the domain (in the TxOPs allocated to it and following the MAC rules of these TxOPs).

3. Conveying topology (routing) information to end point nodes: In order to allow communication in the mesh network, the DM gathers information about the connectivity map of nodes in the domain (i.e. a ‘routing table’ which including all routs from every node to every other node). This routing table is broadcasted to all nodes of the domain and is used by the nodes to know how to ‘reach’ their destination nodes (see more on ‘relaying’ in the next section).

The following Steps 4 through 7 are the steps needed for establishing communication between nodes:

4. Connection setup: A mechanism initiated by the transmitter during which the transmitter and the receiver exchange information about the connection and establish a one way connection (transmitter to receiver). The information exchanged includes control information of the connection, such as usage of acknowledgments, size of FEC block, type of the connection (unicast/multicast/broadcast) and more. Connections may be released by the transmitter or the receiver.

5. Communication using RCM: Once a connection is established, the transmitter can start sending data to the receiver. If the transmitter does not have runtime BATs (bit-loading tables) established with the destination receiver, it will transmit all of the transmissions with a payload transmitted in RCM, that is, using predefined BATs (usually this means loading of 2 bits, i.e. QPSK modulation, uniformly on all SSCs), and repetition.

6. Channel estimation (establishing runtime BATs): This is the process by which a receiver establishes runtime BATs (bit-loading table per subcarrier) with the transmitter. This protocol is very flexible to allow different implementations. For example, the receiver can request the transmitter to transmit probe PHY frames, which are frames in which the entire payload is generated by a pseudorandom sequence generator (each subcarrier is QPSK modulated). Such a receiver will use these probe frames to estimate the channel (and/or noise) and determine the BATs. Another possible receiver implementation will estimate the channel by processing regular data (MSG) PHY frames with their payload transmitted in RCM (e.g. by using channel estimation based on decision-directed processing of the payload). In either case after deriving the BAT, the receiver sends it to the transmitter (along with additional control information such as an identifier of the BAT, called a BAT_ID, the bit-loading grouping) using a special channel estimation management message.

7. Communication with runtime BATs: After a transmitter established a runtime BAT with a receiver, it can use it for communication with the receiver. The BAT_ID identifying the BAT used for modulation of the payload is indicated in the PFH. As mentioned earlier, a specific BAT may be associated with an interval of the AC cycle; hence, a transmitter may hold several BATs (and associated BAT_IDs) with every receiver it communicates with. The transmitter will choose the BAT to use according to the time location of the transmitted frame.

A note regarding security mechanisms in G.hn: If the domain is configured to operate in a secure mode, additional security-related procedures will be required along with the previous: This includes authentication, generation and distribution of encryption keys between nodes and periodical key and authentication updates using a set of authentication and key management (AKM) procedures. All of the traffic in the domain (all of the data and management communication between nodes in the domain) is encrypted (in the LLC sub-layer) using AES-128 encryption. Several encryption modes are possible, such as a mode in which a single encryption key is used per domain or another mode in which every pair of nodes in unicast and nodes of every multicast group use a unique encryption key.

12.2.7 Overview of Some of G.hn’s Mechanisms

This section briefly highlights some of the mechanisms and protocols in G.hn. This is a very brief overview, and the interested reader is referred to the G.hn specifications for further details (see Section 12.2.2 for detailed list of references):

• Acknowledgment and retransmission protocol

In order to increase robustness of transmissions in noisy media, G.hn specifies a mechanism in which the receiver acknowledges reception of segments (LPDUs) of received frames, allowing the transmitter to retransmit those segments which were not received correctly. G.hn specifies two types of acknowledgments: immediate and delayed. With the first one, a receiver receiving a message (MSG) PHY frame replies each frame with an ACK PHY frame (after a predefined IFG). In delayed ACK, the transmission of the ACK frame is deferred to a later TxOP assigned to the receiver. The ACK frame contains information about the segments (LPDUs) which were correctly/incorrectly received (each segment has a CRC attached), in a certain window of segments. The transmitter retransmits segments which were not acknowledged.

• Relaying (at layer 2) of MAPs and data/management frames

In some media types, some of the nodes in the networks might not be ‘visible’ to some nodes (these are referred to as ‘hidden’ nodes) but visible to others. This might be caused by high attenuation in specific links or due to temporary high noise conditions. In order to allow communication between hidden nodes, other nodes must act as relays. G.hn specifies comprehensive relaying mechanisms: For nodes hidden from the DM, MAP relaying is defined in which end point nodes are assigned by the DM to relay the MAPs from time to time (to guarantee that all nodes receive it). In addition, the DM builds and broadcasts the routing table to all nodes of the domain. This table is used by the nodes to know how to ‘reach’ their destination nodes (e.g. node A will know that if it needs to communicate with nodes B, it needs to send its frames through node C, i.e. node C acts as a relay node).

• Multicast protocols

G.hn specifies protocols to support efficient transmission of multicast traffic. A PHY level protocol (‘multicast binding protocol’) enables a transmitter to transmit the same PHY frames to a group of nodes with a common BAT. This protocol also allows member nodes of the multicast group to acknowledge the received data. A DLL level multicast protocol is also defined (allowing multicast traffic to be transmitted over relay nodes).

• PHY frame bursting

In power lines, the bit-loading allocation table (the BAT) may change along the AC cycle, due to the nature of the channel and typical noise (which is usually periodical with a period of a complete or half AC cycle). This means that for a given link, the receiver (and transmitter) usually will maintain a set of BATs, each to be used on a different time portions (called ‘interval’) of the AC cycle. The PHY frame bursting mechanism allows to ‘break’ a long frame into several shorter frames. Each frame in this ‘burst’ may be transmitted with a different BAT. The frames in this burst are transmitted in succession without relinquishing the medium with very small gaps between them. A single ACK frame is used to acknowledge the status of the LPDUs in all of the frames of the burst, if required.

• Bidirectional transmissions

Bidirectional transmissions between two nodes may be used to improve through-put and minimise latency of a traffic that is bidirectional in nature, such as TCP traffic with acknowledgments. With this mechanism, a node originating (sourcing) the bidirectional traffic and the destination node exchange special frames: a bidirectional message (BMSG) frame and a bidirectional acknowledgment (BACK) frame. Both BMSG and BACK carry data and, in the case of acknowledged transmissions, also an acknowledgment on the recently received frame.

• Mitigating interferences from neighbouring (i.e. other G.hn) domains

G.hn specifies a set of tools to mitigate interferences from neighbouring G.hn domains, for example, domains in adjacent apartments in a multi-dwelling unit (MDU) building. Such interference in power lines is common due to inductive propagation between adjacent wirings or due to low attenuation when the networks share common feeder lines. The set of tools include means to quickly detect the existence of neighbouring domains, measure the severity of interferences per node and mitigate the interferences on a node by node basis (some nodes may be interfered and others will not). The mechanism allows the domain to communicate with the other interfering domains and to coordinate transmissions of nodes which strongly interfere with each other.

• Coexistence with alien (non-G.hn) power line networks

When there is a chance that devices of another non-interoperable PLC technology (i.e. non-G.hn) are simultaneously using the same power line cables in the same frequency range, a coexistence mechanism can be used to mitigate the mutual interferences. This mechanism is specified in ITU-T specification G.9972 [6], also known as ‘G. cx’, and is also reviewed in Chapter 10.

12.3 Introduction to G.hn MIMO

A detailed introduction to MIMO signal processing in general, as well as specifically with respect to PLC, has been provided in Chapter 8. For convenience, the following reintroduces some of the basic aspects as well as the mathematical notation used throughout the remainder of this chapter.

12.3.1 Received Signal Model

A MIMO system typically consists of N_T transmitters (or transmission ports) and N_R receivers (or reception ports). At a given time instant, the transmitters send dependent or independent data $(x_{1}, x_{2}, \dots, x_{N_{T}})$ $(x_{1}, x_{2}, \dots, x_{N_{T}})$ over the channel simultaneously and in the same frequency band through N_T transmitters. The composite channel is characterised by a N_R × N_T channel transfer matrix H with entries h_i,j which stand for the transfer response from transmitter j to receiver i.

In OFDM–MIMO systems, this model is used to characterise each one of the individual subcarriers (tones). The following analysis is per subcarrier of the OFDM signal. Thus, all measures should be functions of the frequency (or subcarrier index), but for simplicity of notation, this dependence is omitted. The following relation results from a transmit vector $x = {[x_{1}, x_{2}, \dots, x_{N_{T}}]}^{T}$ $x = {[x_{1}, x_{2}, \dots, x_{N_{T}}]}^{T}$ , a receive vector $y = {[y_{1}, y_{2}, \dots, y_{N_{R}}]}^{T}$ $y = {[y_{1}, y_{2}, \dots, y_{N_{R}}]}^{T}$ and noise vector $n = {[n_{1}, n_{2}, \dots, n_{N_{R}}]}^{T}$ $n = {[n_{1}, n_{2}, \dots, n_{N_{R}}]}^{T}$ :

$y = H x + n .$ $y = H x + n .$

We will also denote by Λ the cross-correlation matrix of the noise components:

$Λ = E {n \cdot n^{H}},$ $Λ = E {n \cdot n^{H}},$

where $E {\cdot}$ $E {\cdot}$ is the mathematical expectation operator for random variables.

12.3.2 Closed-Loop Transmit Diversity Schemes

Turning to practical considerations in the process of MIMO scheme selection, closed-loop transmit diversity schemes (with 1 SS, 2 Tx ports) appear to be very useful for wireless fading channels [7]. For PLC, where radiation limits apply, these advantages are undermined. For example, for the beamforming configuration (beamforming in the case of 1 SS is sometimes referred to as spot beamforming, in contrast to beamforming with 2 SSs which is referred to as eigenbeamforming and is a spatial multiplexing (SM) scheme), one may not use half the single-input single-output (SISO) transmit power (Tx power reduced by 3dB) on each one of the two transmit ports due to the spatial directivity of the radiation pattern: constructive superposition of the signals at the receiver wires may also be achieved on some other point in space. Thus, generally speaking, in transmit beamforming, the restriction of the PSD sum conveyed over the two wire pairs to that of the SISO transmission is no longer satisfactory, and the relations between the MIMO and SISO systems should apply to the transmit voltages instead. This limitation makes the transmit beamforming scheme useless and degenerates the best beamforming configuration (with optimum power allocation) to a simple one-pair transmitter (selecting the best transmitter). Further treatment on beamforming and electromagnetic compatibility may be found in Chapter 16.

12.3.3 Open-Loop Transmit Diversity Schemes

Similarly, Alamouti’s space–time code [8] is useful for time-varying channels without channel state information at the transmitter, in which it may exhibit a significant diversity gain. However, assuming that the channel is known and that the transmitter adapts its transmission parameters to the (slowly) varying channel conditions, it is better to deliver all of the allowed power to the best transmitter: Alamouti’s space–time code is inferior to a single-port transmission (with per subcarrier Tx selection) with an MRC receiver, assuming an underlying total power constraint.

12.3.4 Spatial Multiplexing MIMO with Precoding (Closed-Loop MIMO)

In a precoding-based SM MIMO system, the receiver estimates the channel response matrix and conveys some sort of channel state information (this is usually called a ‘precoding matrix’), derived from this matrix, to the transmitter via a feedback channel. The transmitter uses this channel state information (i.e. the precoding matrix) to adapt (‘precode’) its transmissions to the varying channel conditions. The scheme, also known as ‘closed-loop MIMO’ (due to the feedback from the receiver to transmitter), provides a good trade-off between receiver complexity and the ability to nearly achieve the channel capacity, compared to ‘open-loop’ MIMO schemes.

NOTE: The previous description assumes that the transmitter gains access to the precoding matrix through feedback from the receiver. In a general description of a MIMO precoding scheme, there is another alternative. Theoretically (and under some circumstances), many channels are reciprocal, so the transmitter could estimate the channel on the other direction (based on frames it receives from the other node on the other direction) and use it to precode the data it transmits. This is sometimes referred to as ‘open-loop’ precoding (do not confuse it with open-loop MIMO which usually refers to SM) or ‘implicit feedback’. In practice, channel reciprocity is rather difficult to achieve: it requires some calibrations which might increase the overhead of the transmitted PHY frames. In addition, transmit and receive impedances in PLC are different, and for reciprocity to hold in PLC channels, they must be the same. Therefore, in principle, it seems this method is not viable in PLC.

In order to derive the MIMO precoding scheme, let us take the channel response matrix H and transform it to its singular value decomposition (SVD):

$H = U D V^{H},$ $H = U D V^{H},$

where $U \in C^{N_{R} \times N_{R}}$ $U \in C^{N_{R} \times N_{R}}$ and $V \in C^{N_{T} \times N_{T}}$ $V \in C^{N_{T} \times N_{T}}$ are unitary (i.e. $U^{- 1} = U^{H}, V^{- 1} = V^{H}$ $U^{- 1} = U^{H}, V^{- 1} = V^{H}$ ) and $D \in ℜ^{N_{R} \times N_{T}}$ $D \in ℜ^{N_{R} \times N_{T}}$ is nonnegative and diagonal. The diagonal entries of the matrix D are the non-negative square roots of the eigenvalues of HH^H

Using the following (information lossless), orthogonal transformation,

$\tilde{y} = U^{H} y, \tilde{x} = V^{H} x, \tilde{n} = U^{H} n,$ $\tilde{y} = U^{H} y, \tilde{x} = V^{H} x, \tilde{n} = U^{H} n,$

on the system model described in Section 12.3.1,

$y = H x + n,$ $y = H x + n,$

results in the following equivalent model:

$\tilde{y} = D \tilde{x} + \tilde{n} .$ $\tilde{y} = D \tilde{x} + \tilde{n} .$

The practical interpretation of the previous transformation and models is as follows:

1. The receiver estimates the channel response matrix H (a process called ‘channel estimation’).

2. The receiver then calculates the precoding matrix V, for example, by performing the SVD operation on the matrix H (H = UDV^H).

3. The receiver sends the precoding matrix V (or some representation of it) to the transmitter via a feedback channel.

4. The transmitter performs precoding of the data, x, it needs to send to the receiver, using the precoding matrix V, that is, performs $x = V \tilde{x}$ $x = V \tilde{x}$ and transmits x.

5. At the receiver, the following signal is received: y = Hx + n.

6. The receiver applies the matrix U^H on the received signal y:

$\begin{array}{l} \tilde{y} = U^{H} y, \\ = U^{H} H x + U^{H} n, \\ = U^{H} U D V^{H} V \tilde{x} + U^{H} n, \\ = D \tilde{x} + \tilde{n} . \end{array}$ $\begin{array}{l} \tilde{y} = U^{H} y, \\ = U^{H} H x + U^{H} n, \\ = U^{H} U D V^{H} V \tilde{x} + U^{H} n, \\ = D \tilde{x} + \tilde{n} . \end{array}$

7. Since D is diagonal, both channels are decoupled and the receiver can continue with the decoding process on these two separate channels. Since U is unitary, the noise power is not increased.

A note regarding the additive noise: clearly,

$E {\tilde{n} \cdot {\tilde{n}}^{H}} = E {U^{H} n \cdot n^{H} U} = U^{H} Λ U .$ $E {\tilde{n} \cdot {\tilde{n}}^{H}} = E {U^{H} n \cdot n^{H} U} = U^{H} Λ U .$

Thus, if Λ = I, then the transformed noise vector also has this unity covariance matrix. In the general case, the additive noise might not be white; therefore, a whitening filter will be needed as part of the processing. From here onward, we can absorb the whitening filter into the channel matrix response and thus assume that Λ = I. We henceforth refer to the concatenation of the channel matrix response and the whitening filter as the equivalent channel response.

The previous orthogonal transformation decomposes the channel into independent parallel channels:

$\tilde{y} = λ_{i}^{1 / 2} {\tilde{x}}_{i} + {\tilde{n}}_{i}, 1 \leq i \leq min (N_{R}, N_{T}),$ $\tilde{y} = λ_{i}^{1 / 2} {\tilde{x}}_{i} + {\tilde{n}}_{i}, 1 \leq i \leq min (N_{R}, N_{T}),$

where

λ_i is an eigenvalue of HH^H

min(N_R, N_T) is the rank of the channel matrix (assuming it is full rank), which is equal to the maximal number of SSs (which for the case of the MIMO PLC channel equals 2).

The capacity of each of the component channels is given by

$C_{i} = \log_{2} (1 + P_{i i} λ_{i}), P_{i i} \equiv E {{| x_{i} |}^{2}} .$ $C_{i} = \log_{2} (1 + P_{i i} λ_{i}), P_{i i} \equiv E {{| x_{i} |}^{2}} .$

In order to maximise the total capacity of the channel, we need to maximise the sum mutual information. This maximisation results in the optimum power allocation needed for each of the constituent channels. There are several results known in the literature for this optimisation:

• Assuming that x_i’s are chosen to be independent, zero-mean Gaussian variables, the optimum power allocation is obtained by the known ‘waterfilling’ calculation [9].

• If, however, x_i’s are chosen to be discrete signalling constellations such as m-PSK or m-QAM in lieu of the ideal Gaussian signals, the optimum power allocation is obtained by the mercury/waterfilling calculation [10].

Note that experimental treatment on PLC channel capacity has been presented in Chapter 9.

SM MIMO with precoding approaches the channel capacity provided that the channel variations in time are not too rapid. This is indeed the case in PLC channels, as the PLC channel’s transfer function is quasi-static; it varies only slowly with time, except for cases in which the power line channel topology is changed (e.g. an electrical device is plugged-in in the vicinity of the considered sockets). In general, calculation of the precoding matrix requires SVD of the equivalent channel matrix response (including the whitening filter). The precoder scheme also facilitates the detection of high-order MIMO schemes. However, its drawbacks are the need to communicate the precoder coefficients to the transmitter (closed-loop MIMO configuration), the rate loss incurred by this communication and its limited capability to cope with channel variations. Likewise, on the practical side, it necessitates a rather large memory at the transmitter end in order to accommodate the precoder coefficients for all of the links from one node to all of the other domain nodes.

12.3.5 Spatial Multiplexing MIMO without Precoding (Open-Loop MIMO)

An alternative to the SM MIMO precoding (closed-loop) scheme is the non-precoded SM MIMO (open-loop) scheme. Such a MIMO scheme was first proposed in the late 1990s and was known as the Bell Labs Layered Space-Time (BLAST) scheme. In these SM MIMO schemes, the transmitter has no knowledge on the channel and the transmission is rather simple: independent data streams are transmitted through the multiple Tx ports thus achieving spatial diversity (increased throughput).

Open-loop schemes which use FEC encoding prior to the MIMO mapping include two variants: vertical and horizontal MIMO schemes. Vertical encoding specifies that one FEC block is encoded and multiplexed onto all of the SSs for spatial diversity. Horizontal encoding specifies that separate FEC blocks are encoded for each of the parallel SSs separately. Block diagrams of vertical and horizontal MIMO transmitters are given in Figures 12.14 and 12.15, respectively (Note: The ‘streams to Tx port mapping’ block in the simplest case is an identity mapping, i.e. steam 1 is mapped to Tx port 1).

In open-loop schemes, most of the MIMO processing burden is placed on the receiver side. The receiver usually tries to de-multiplex the SSs in order to detect the transmitted symbols. Simplistically, there are a variety of decoding techniques to achieve this, starting from simple and up to complex ones, to name a few: zero-forcing (ZF) that uses simple matrix inversion but results in poor performance when the channel matrix is ill conditioned; minimum mean square error (MMSE), which is more robust in that sense but provides limited enhancement if knowledge of the noise/interference is not used; and maximum likelihood (ML), which is optimal in the sense that it compares all possible combinations of symbols but can be too complex, especially for high-order modulations.

FIGURE 12.14
Vertical SM MIMO (open-loop) transmission.

FIGURE 12.15
Horizontal SM MIMO (open-loop) transmission.

Practically, devising capacity-achieving and non-complex receivers for the open-loops schemes is not a trivial task: By contrast to single-port transmission, the capacity of a (vertical) coded MIMO transmission scheme (with a bit-interleaved coding scheme) cannot be approached by concatenating a MIMO detector that generates the log-likelihood ratio (LLR) of the coded bits and a FEC decoder, as the LLRs of the constituent bits of the symbol pair are no longer independent. One alternative solution is to jointly decode the signals from the two wire pairs using a ‘turbo equalisation’ scheme, where information is iteratively passed between a soft-input-soft-output MIMO detector and a soft-input-soft-output FEC decoder.

As an alternative to the vertical SM MIMO scheme with a turbo equalisation receiver, one can use the horizontal SM MIMO transmission scheme with a successive interference cancellation (SIC) receiver: As separate encoding is used at the transmitter, the various codewords in the horizontal MIMO scheme may be decoded successively. A SIC receiver of a horizontally encoded MIMO signal decodes one stream, re-encodes it and subtracts the effect of this codeword from the received signal. The resulting signal, after cancellation (subtraction), is used to detect the second SS. In general, for a higher-order horizontal MIMO system, this procedure is repeated iteratively, where, in each step, the receiver decodes one stream after subtracting the effect of previously decoded streams and treating the effect of all other streams as coloured noise. On the other hand, the horizontal scheme with the SIC receiver suffers from several drawbacks (relative to the vertical one): The scheme requires substantial memory needed to store the received signal points associated with the second decoded stream till the first one is decoded and its effect on the buffered stream is subtracted. Decoding latency is also induced by the SIC policy, which might require a larger IFG period to compensate for the processing latencies in the receiver. It also requires a rather complex scheduling of the FEC decoding.

In conclusion, assuming that the MIMO transmitter is expected to meet the same radiation regulation and that the SISO PSD specified in G.hn was imposed by these requirements (see Section 12.2.4.5.10), the MIMO configuration that seems to hold the greatest promise for power line is SM (with or without precoding) along with the constraint that the sum of PSDs transmitted from the two wire pairs should be equal to the specified SISO PSD. This conclusion is consistent with the findings reported in [11], where the attainable throughputs of the different mentioned MIMO schemes are compared.

12.3.6 Basic Requirements from G.hn MIMO

The following requirements were used to design the various elements of the G.hn MIMO transmission schemes and frame format:

1. Optimally exploiting the MIMO PLC channel (increasing the throughput and coverage): The basic design goal was to design a MIMO transmission scheme which, combined with proper processing in the receiver, will optimally exploit the properties of the MIMO PLC channel, thus providing an increased data rate and enhanced connectivity (i.e. service coverage) of the home network. As previously explained, the spatial diversity of the MIMO PLC channel is 2, meaning that 2 SSs can be transmitted over the channel independently (hence, theoretically doubling the throughput/capacity of the channel compared to single-port transmissions).

2. Interoperability with legacy, non-MIMO G.hn nodes: A fundamental assumption made during the development of G.hn MIMO was that a G.hn network can be composed of legacy (native) G.hn nodes, that is, nodes not supporting G.hn MIMO and nodes supporting G.hn MIMO. All of these devices need to interoperate (although clearly the full benefits of the MIMO transmissions will be exhibited when two G.hn MIMO devices are communicating). Two basic requirements result from this assumption:

a. Native G.hn transceivers (i.e. non-MIMO transceivers complying with G.9960 and G.9961) and G.hn MIMO transceivers (complying with G.9963) need to be able to interoperate when they operate on the same wires and belong to the same domain.

b. Transmissions from G.hn MIMO transceivers will not degrade the performance of native G.hn transceivers, when operating on the same lines (e.g. allowing non-MIMO G.hn nodes to track the MAC cycle grid in the presence of MIMO transmissions).

These two requirements had implications on both the selected MIMO frame structure and the various options for transmitting the payload, as explained later on.

3. Facilitating acquisition of the MIMO channel at the receiver: Acquisition of PHY frames at the receiver includes several mechanisms, such as detection of the frame (preamble), acquiring gain, frequency and timing synchronisation and obtaining initial channel estimates. A basic requirement related to these acquisition algorithms is that the G.hn MIMO specification should provide all the tools required to perform these acquisitions on a per frame basis (i.e. not relying only on probe frames), in order to cope with rapid variations of the channel response and noise. For the special case of the MIMO PLC channel, care should be taken for the following two acquisition mechanisms:

a. Tuning the AGC: This requires a training sequence which will allow the receiver to set the AGC of the two reception ports, that is, transmission of independent training sequences on the two transmission ports, preparing for receiving the payload which is transmitted over the two transmission ports.

b. MIMO channel response estimation: Providing the tools to allow estimating the full channel response of the MIMO PLC channel (i.e. the four coefficients of the channel matrix), prior to reception of the payload.

12.4 G.hn MIMO

This section begins with describing the road leading to full G.hn MIMO implementations: Although the native G.hn specifications do not mention MIMO transmissions, some implementations which include variants of MIMO schemes are possible and were indeed implemented. Section 12.4.1 describes these possible schemes, paving the way toward full MIMO implementations.

The section continues with describing the various elements of G.hn MIMO: The first element described in Section 12.4.2 is the structure (format) of the PHY frame supporting the MIMO transmissions. The PHY frame for MIMO transmissions was especially designed so that it will accommodate transmissions to both legacy (non-MIMO) G.hn devices and to MIMO G.hn devices, thus allowing for interoperability between these two device types. The description includes some of the criteria used for designing the frame format.

The second element, described in Section 12.4.3, is the structure of the G.hn MIMO transceiver with the new blocks added to enhance the G.hn transceiver to support operation over the MIMO PLC channel.

Finally, Section 12.4.4 describes how the MIMO PHY frame and the transceiver elements are being practically used to implement the different supported transmission schemes used to transmit the payload. A MIMO G.hn node (i.e. a node compliant with the G.9963 specification) is required to be capable of communication with both legacy (non-MIMO) G.hn nodes and MIMO G.hn nodes. This means that a MIMO G.hn node is able to transmit frames using two transmission options: transmissions in which the payload is created as a single SS, for transmissions to legacy (non-MIMO) G.hn nodes (or for cases in which a third conductor is not available), and transmissions in which the payload is created as two SSs, for transmissions to other MIMO G.hn nodes. Both of these options include several possible transmission schemes answering the requirements and allowing different implementations with different complexities, as described in the section.

12.4.1 Road toward a Full G.hn MIMO PLC System

The legacy G.hn standard specifies transmission over a single transmission port (at any given time). The standard does not, however, specifically define any specific mapping of this transmission port to actual wire pairs. The G.hn standard (as any other standard) is focused on specifying the transmitter side and does not directly specify how the receiver should be structured. Receiver structures are left for the implementers to decide on.

Traditional PLC transceivers used only a single transmission port and a single reception port for communication, where these ports are traditionally connected to the phase-neutral (P-N) pair of conductors. Such devices can be referred to as SISO devices. Since, as mentioned earlier, the structure of the receiver is not dictated by the standard, a vendor may choose to implement a receiver receiving from multiple ports, either selecting the better port(s) or combining several ports, thus exploiting the receive diversity in the MIMO PLC channel, even when the transmission is done through a single Tx port. Such devices can be referred to as single-input multiple-output (SIMO) devices. Other types of devices, still compliant with legacy non-MIMO PLC standards, such as G.hn, may employ different transmit diversity techniques at the transmission ports. For example, a transceiver may be connected to two wire pairs and transmit on one of them at any given time, where the selection may be left for the transmitter or it may be based on some channel quality measures delivered by the receiver to the transmitter (such feedback is proprietary, i.e. not specified in the standard). The receiver can either use a single Rx port (tuned to the same Tx port) or use multiple Rx ports. Topology wise, such schemes can be considered as a ‘MIMO’ scheme, although they will not achieve any spatial or capacity gain since they are basically a single SS scheme. They will be able to achieve some diversity gain (either transmit or/and receive diversity gains).

All of variants of transceivers mentioned previously are not full MIMO transceivers and will obviously not reach the full potential gain of MIMO systems since inherently any scheme based on the legacy G.hn specifications is limited to being a single SS scheme. However, these variants can be seen as a road paving the way for full G.hn MIMO transceivers, as described in the following sections.

12.4.2 G.hn MIMO PHY Frame

12.4.2.1 Structure of the G.hn MIMO PHY Frame

The general structure of the frames used for MIMO transmissions is illustrated in Figure 12.16.

The MIMO transmission frame format adheres to the following:

• The entire frame, that is, the preamble/header/additional channel estimation (ACE) symbol/payload, is transmitted simultaneously on both Tx ports.

• The preamble and the header symbol transmitted on the second Tx port are copies of the preamble and header symbol(s) transmitted on the first Tx port.

• For the case where the payload is created as two SSs, one ACE symbol is added to the frame, after the header. The ACE symbol does not carry data but rather a pseu-dorandom sequence of constellation points (2 bits per subcarriers), used to assist the receiver in obtaining estimates of the MIMO channel response (as explained later on). It is constructed exactly as probe symbols (the payload of the probe frames). The ACE symbol transmitted on the second Tx port is an inverted version of the ACE symbol transmitted on the first Tx port (i.e. for each time sample of the ACE, $x_{2}^{A C E} = - x_{1}^{A C E}$ $x_{2}^{A C E} = - x_{1}^{A C E}$ , where the subscripts 1 and 2 denote the SS number).

• The payload may be created as either two SSs (indicated by setting a field called MIMO_IND in the PFH to 1) or a single SS (indicated by setting the field MIMO_IND in the PFH to 0).

• Transmissions on the second Tx port are done with a cyclic shift with respect to the transmission on the first Tx port.

FIGURE 12.16
Format of the G.hn MIMO PHY frame.

12.4.2.1.1 Purpose of the Cyclic Shift

The cyclic shift on the second Tx port is needed for AGC setting at the receiver: It is aimed at guarantying that the two versions of the underlying preamble signal transmitted through the two wire pairs are practically uncorrelated so that the received signal power during preamble transmission is the simple sum of the power received from each one of the two transmitting wire pairs (the appealing choice for a MIMO preamble signal in greenfield technologies is based on a combination of independent signals transmitted each through one of the different Tx ports. Albeit, such a selection for the MIMO scheme for G.hn would not be interoperable with legacy G.hn devices which employ detection algorithms based on cross-correlation).

12.4.2.1.2 Purpose of the Added ACE Symbol

The addition of this symbol is aimed at allowing the receiver to estimate the full MIMO channel. As mentioned earlier, one of the requirements while designing G.hn MIMO was to allow the receiver to derive MIMO channel estimates on a frame-by-frame basis, which then may be used by the receiver for decoding the payload. On the other hand, in order not to decrease the efficiency of MIMO transmissions, any additional overhead to the PHY frame should be minimised. For this reason the G.hn MIMO spec facilitates the following MIMO channel estimation scheme:

1. The receiver produces an initial channel estimate based on the received header (and may be the last part of the preamble). The received signal at Rx port 1 and 2 is as follows:

$\begin{array}{l} y_{1}^{h e a d e r} = h_{11} \cdot x_{1}^{h e a d e r} + h_{12} \cdot x_{2}^{h e a d e r} + n_{1} = (h_{11} + h_{12}) \cdot x^{h e a d e r} + n_{1}, \\ y_{2}^{h e a d e r} = h_{21} \cdot x_{1}^{h e a d e r} + h_{22} \cdot x_{2}^{h e a d e r} + n_{2} = (h_{21} + h_{22}) \cdot x^{h e a d e r} + n_{2}, \\ i n the pervious: x_{1}^{h e a d e r} = x_{2}^{h e a d e r} = x^{h e a d e r}, \end{array}$ $\begin{array}{l} y_{1}^{h e a d e r} = h_{11} \cdot x_{1}^{h e a d e r} + h_{12} \cdot x_{2}^{h e a d e r} + n_{1} = (h_{11} + h_{12}) \cdot x^{h e a d e r} + n_{1}, \\ y_{2}^{h e a d e r} = h_{21} \cdot x_{1}^{h e a d e r} + h_{22} \cdot x_{2}^{h e a d e r} + n_{2} = (h_{21} + h_{22}) \cdot x^{h e a d e r} + n_{2}, \\ i n the pervious: x_{1}^{h e a d e r} = x_{2}^{h e a d e r} = x^{h e a d e r}, \end{array}$

since the same header data are transmitted over SSs 1 and 2. Hence, the receiver can only derive channel estimates for the composite channel (h₁₁ + h₁₂) from receiving the header at Rx port 1 and (h₂₁ + h₂₂) from receiving it in Rx port 2.

2. The receiver produces another set of channel estimates based on the received ACE symbol. The received signal at Rx port 1 and 2 is as follows:

$\begin{array}{l} y_{1}^{A C E} = h_{11} \cdot x_{1}^{A C E} + h_{12} \cdot x_{2}^{A C E} + n_{1}, \\ = h_{11} \cdot x^{A C E} + h_{12} \cdot (- x^{A C E}) + n_{1} = (h_{11} - h_{12}) \cdot x^{A C E} + n_{1}, \\ y_{2}^{A C E} = h_{21} \cdot x_{1}^{A C E} + h_{22} \cdot x_{2}^{A C E} + n_{2}, \\ = h_{21} \cdot x^{A C E} + h_{22} \cdot (- x^{A C E}) + n_{2} = (h_{21} - h_{22}) \cdot x^{A C E} + n_{2}, \\ i n the pervious: x_{1}^{A C E} \equiv x, x_{2}^{A C E} \equiv - x^{A C E}, \end{array}$ $\begin{array}{l} y_{1}^{A C E} = h_{11} \cdot x_{1}^{A C E} + h_{12} \cdot x_{2}^{A C E} + n_{1}, \\ = h_{11} \cdot x^{A C E} + h_{12} \cdot (- x^{A C E}) + n_{1} = (h_{11} - h_{12}) \cdot x^{A C E} + n_{1}, \\ y_{2}^{A C E} = h_{21} \cdot x_{1}^{A C E} + h_{22} \cdot x_{2}^{A C E} + n_{2}, \\ = h_{21} \cdot x^{A C E} + h_{22} \cdot (- x^{A C E}) + n_{2} = (h_{21} - h_{22}) \cdot x^{A C E} + n_{2}, \\ i n the pervious: x_{1}^{A C E} \equiv x, x_{2}^{A C E} \equiv - x^{A C E}, \end{array}$

since the ACE symbol transmitted on SS 2 is an inverted version of the ACE symbol transmitted over SSs 1. Hence, the receiver can derive channel estimates for the composite channels, (h₁₁ – h₁₂) and (h₂₁ – h₂₂) from receiving the ACE at Rx port 1 and 2, respectively.

3. The extraction of the individual channel responses for the complete MIMO channel matrix can now be derived directly by subtraction and summation of the two composite responses obtained at steps 1 and 2, for each of the received port.

12.4.2.2 Design Aspects of the G.hn MIMO PHY Frame

This section provides some insights regarding the design criteria and performance merits of the PHY frame structure selected for G.hn MIMO:

Interoperability with legacy G.9960/1 (non-MIMO) devices: The cyclic shift scheme is, by design, fully interoperable with legacy G.hn devices. This is due the fact that the frames start with the legacy G.hn preamble and header. This interoperability is important for the case of a domain which includes both MIMO and non-MIMO G.hn nodes. In such a case when two MIMO nodes communicate with each other using a shared MAC (STxOP), all nodes including non-MIMO nodes need to be able to detect the preamble and decode the header of PHY frames so they will be able to track the MAC cycle grid (‘virtual carrier sensing’). Decoding the header is important since it contains the ‘duration’ field, describing the duration of the PHY frame. The impact of the cyclic shift on the detection performance of legacy G.hn devices (passively listening to MIMO transmissions for virtual carrier sensing) is examined in the following text.

Selecting the value of the cyclic shift applied to the second Tx port: This selection involves two adverse considerations: On the one hand, correct AGC setting for receiving a MIMO payload transmission of two independent SSs is in favour of large values of cyclic shift (larger than the typical delay spread of the power line channels). On the other hand, large values of the cyclic shift widen the duration of the composite channel response as sensed during preamble transmission and blunt the sharp, single peak nature of the cross-correlation measure that is calculated by the frame (preamble) detector in the receiver, thus degrading its performance.

The selection of the cyclic shift value was the result of an evaluation which was based on real-field MIMO channels measurements. This database included 72 MIMO power line channels measured in 13 homes in North America (6 channels measured per home). The evaluation showed the following:

1. The AGC mismatch factor is bounded by around ±1dB for CS > T_S/8 (T_S is the time duration of a preamble’s mini-symbol, T_S = 5.12 μs) and ±0.5 dB for CS > T_S/4.

2. The performance degradation of a cross-correlation-based frame (preamble) detector due to the cyclic shift depends on the actual implementation of the detector, its threshold setting and target miss-detection and false alarm probabilities. An evaluation (see the next paragraph) showed that a cyclic shift of T_S/8 results in an acceptable degradation. Larger values of the cyclic shift result in relatively significant degradation (and the selection of CS = T_S/2 renders the detector useless).

According to these results the cyclic shift in G.hn MIMO was set to a value of T_S/8 (= 0.64 μs), which reflects the best compromise between the two conflicting design targets.

What is the performance impact of using the MIMO preamble on a legacy G.hn device that is listening to a MIMO transmission for virtual carrier sensing purposes?

In order to answer this question, real-field MIMO channel measurements (same measurement database mentioned in the previous paragraph) were used to simulate the effect of the cyclic shift. These simulations assumed 3 dB reduction of the transmit power through each wire pair of the MIMO preamble relative to the legacy G.hn preamble so that the total transmit power is preserved. As we are interested in the performance of legacy SISO receivers, the analysis evaluated the performance of a single-port receiver coupled to the phase-neutral (marked as ‘P-N’ in Figures 12.17 and 12.18) wire pair only.

From the detection performance perspective, the new preamble signal may exhibit either performance gain or loss relative to the legacy preamble. On the one hand, it enjoys diversity and robustness due to the simultaneous transmission through the second wire pair, but on the other hand, it experiences 3 dB power cutback of the legacy transmission through the P-N wire pair.

For each channel, the sensitivity loss of a detector connected to the P-N wire pair, under the MIMO cyclic shift transmission scheme, was checked, relative to the legacy G.hn preamble transmission scheme (i.e. transmission through the P-N wire pair only). The sensitivity loss is defined as the difference in noise levels required to achieve the same detection performance (misdetection and false alarm rates) for the MIMO and legacy preambles using the same cross-correlation-based detector. We note that negative loss means performance gain of the detector when operated with the MIMO preamble relative to its performance when detecting the legacy G.hn preamble. This gain is ascribed to the use of the second wire pair. Figure 12.17 presents the results for all the measured MIMO channels, for the case of cyclic shift of T_s/8 = 0.64 μs.

Figure 12.18 presents the same results but with classification of the MIMO channels to one of three groups based on the average attenuation of the legacy channel connecting the P-N wire pair at both ends of the communication channel. This measure is indicative of the SNR of the received legacy preamble.

Figure 12.17 shows that though in some channels the MIMO preamble exhibits better performance, on the average, it is slightly degraded compared to the legacy preamble. However, looking at Figure 12.18, one can see that there is an outstanding correlation between the performance gain/loss of the frame detector for the MIMO cyclic shift transmission scheme (relative to its performance under the legacy G.hn preamble) and the quality (SNR) of the original P-N wire pair. For the 33% worst channels, the MIMO preamble exhibits 0.9 dB performance gain relative to the detection performance of the legacy preamble over the same channels. On the 33% best channels, the MIMO preamble incurs on the average 1.7 dB performance loss. On the remaining channels (those with moderate reception power), the MIMO preamble incurs an average loss of 0.7 dB. In other words, for poor channels, the frame detector exhibits better performance when operated with the MIMO preamble (with the cyclic shift format) than its performance under processing the legacy G.hn preamble. This means that for these channels, the benefit of the use of the second wire pair is larger than the penalty of the 3 dB power reduction. However, over the good channels, the frame detector shows inferior performance when it processes the proposed MIMO preamble. Yet, over these channels the detector operates very reliably and enjoys a significant noise margin and this loss is not reflected by any practical implication.

FIGURE 12.17
Detection loss of the MIMO preamble.

FIGURE 12.18
Detection loss of the MIMO preamble with channel segmentation.

To summarise, the results show that the channel coverage of the frame detector for MIMO with the cyclic-shift-based preamble is larger than its counterpart channel coverage for the detection of the legacy preamble. As this is the prominent figure of merit of the preamble signal, the degradation in the SNR experienced by the detector in good channels does not incur any practical loss. It seems that for the challenging (poor) channels, on the average, the proposed MIMO preamble will not degrade the performance of the frame detector but rather offer some gain (better detection performance) despite the 3 dB power reduction.

12.4.3 G.hn MIMO Transceiver

The block diagram of the PHY of the G.hn transceiver (transmitter) is presented in Figure 12.19.

FIGURE 12.19
Functional model of the PHY of a G.hn MIMO transceiver.

The description hereafter will focus on the blocks unique to the MIMO processing and the changes needed in other blocks needed for MIMO operation (i.e. the appropriate extensions needed to have them work on 2 SSs).

12.4.3.1 Data Scrambling and FEC Encoding of the Header and Payload

Both the header and payload data (the MPDU coming from the DLL) are scrambled, and LDPC encoded exactly the same way as in a legacy G.hn transceiver.

12.4.3.2 Spatial Stream Parsing (of the Payload)

The SSs parser works on the output of the FEC LDPC encoder of the payload. There are two cases:

1. Whenever the payload is created as a single SS, the parser does not do anything, that is, delivers the encoded payload block to its output as is.

2. Whenever the payload is created as two SSs, the parser parses the encoded pay load block into two SSs in the following way: The parser assigns (groups of) bits alternately to each stream at the subcarrier level according to the bit loading on each stream. Defining $b_{i}^{(q)}$ $b_{i}^{(q)}$ as the number of data bits to be loaded to subcarrier i of SS q according to the BAT, the SS parser assigns the first $b_{0}^{(1)}$ $b_{0}^{(1)}$ bits at its input to SS 1, the next $b_{0}^{(2)}$ $b_{0}^{(2)}$ bits at its input to SS 2, the next $b_{1}^{(1)}$ $b_{1}^{(1)}$ bits at its input to SS 1, the next $b_{1}^{(2)}$ $b_{1}^{(2)}$ bits at its input to SS 2 and so on (if $b_{i}^{(q)}$ $b_{i}^{(q)}$ is zero, no data bits are assigned to subcarrier i of SS q).

12.4.3.3 Tone Mapping

The tone mapper operates independently on each one of the incoming SSs, dividing the incoming streams of bits of the header and payload (of each SS) into groups of bits according to the BAT being used for that SS (i.e. BAT^(q) for SS q, q = 1, 2) and the subcarrier grouping (the BAT grouping is identical for the two SSs), and associates each group of bits with specific subcarriers onto which these groups shall be loaded. This information is passed to the constellation encoder.

12.4.3.4 Bit Generation for Inactive Subcarriers, Constellation Mapping and Scaling and Constellation Scrambling

For MIMO, the LFSR used to generate bits for inactive and partially loaded subcarriers operates on each SS separately (the specification allows implementing this generator with either two separate LFSRs or a single LFSR).

The constellation mapping and scaling is also performed independently on each SS, associating group of bits of a specific SS, with the I (in-phase component) and Q (quadrature-phase component) values of a scaled constellation diagram (for a specific subcarrier i, different constellations may be used for SS 1 and SS 2).

The operation of the constellation mapper is identical to that used for the legacy G.hn transceiver, where the same phase shift is applied to the constellation points of both SSs per the same subcarrier (i.e. the LFSR output per a subcarrier is used to determine the phase shift applied to the constellation points of both SSs associated with the specific subcarrier).

12.4.3.5 Tx Port Mapping (Including Precoding)

The Tx port mapper converts the SSs at its input into transmit streams at its output. The inputs to the mapper are either a single or two SSs coming from the constellation scrambler. The outputs are the transmit streams which are transformed to time-domain samples by the OFDM Modulator and connected to Tx ports. The Tx port mapper operates on a per subcarrier basis. On each subcarrier, it maps a single or a pair of constellation points assigned to the SSs of the subcarrier, to modified pair of signals which are connected (after OFDM modulation, i.e. IDFT) to Tx ports, according to a Tx port mapping allocation table (MAT) which the receiver sent. The operation of the Tx port mapper, for subcarrier i, is described mathematically as follows:

$[\begin{matrix} S_{o u t, i}^{(1)} \\ S_{o u t, i}^{(2)} \end{matrix}] = [\begin{matrix} T P M_{11, i} & T P M_{12, i} \\ T P M_{21, i} & T P M_{22, i} \end{matrix}] \cdot [\begin{matrix} S_{i n, i}^{(1)} \\ S_{i n, i}^{(2)} \end{matrix}], i = 0, \dots ., N - 1 .$ $[\begin{matrix} S_{o u t, i}^{(1)} \\ S_{o u t, i}^{(2)} \end{matrix}] = [\begin{matrix} T P M_{11, i} & T P M_{12, i} \\ T P M_{21, i} & T P M_{22, i} \end{matrix}] \cdot [\begin{matrix} S_{i n, i}^{(1)} \\ S_{i n, i}^{(2)} \end{matrix}], i = 0, \dots ., N - 1 .$

where

$S_{i n, i}^{(q)}$ $S_{i n, i}^{(q)}$ is the input signal associated with subcarrier i of SS q (in the case where only a single SS is used $S_{i n, i}^{(2)}$ $S_{i n, i}^{(2)}$ = 0)

$S_{o u t, i}^{(k)}$ $S_{o u t, i}^{(k)}$ is the output signal associated with subcarrier i of transmit stream k, and the Tx port mapping matrix (TPM) for subcarrier i denoted TPM_t is

$T P M_{i} = [\begin{matrix} T P M_{11, i} & T P M_{12, i} \\ T P M_{21, i} & T P M_{22, i} \end{matrix}], i = 0, \dots, N - 1,$ $T P M_{i} = [\begin{matrix} T P M_{11, i} & T P M_{12, i} \\ T P M_{21, i} & T P M_{22, i} \end{matrix}], i = 0, \dots, N - 1,$

where its elements TPM_kq,i denote the mapping from SS q to transmit stream k for subcarrier i.

12.4.3.5.1 Specific Tx Port Mapping Matrices (per a Single Subcarrier i)

The specific Tx port mapping for the different MIMO schemes and different mapping options, for a specific subcarrier i, is described by specific mapping matrices (the vector describing the complete allocation of subcarrier indices and Tx port mappings for all subcarriers in the frequency axis is described by the MAT which is described in Section 12.4.3.6):

• The ‘direct’ mapping: for copying a single input, to the two Tx ports (e.g. for spatial mapping (SM) of without precoding)

$T P M # 0 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}] .$ $T P M # 0 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}] .$

• The ‘duplication’ mapping: Used for copying a single input, to the two Tx ports (e.g. for mapping of the preamble and header)

$T P M # 1 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ 1 & 0 \end{matrix}] .$ $T P M # 1 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ 1 & 0 \end{matrix}] .$

• The ‘duplicate and negate’ mapping: Used for copying a single input, to the two Tx ports with the second Tx port inverted (e.g. for mapping of the ACE symbol)

$T P M # 2 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ - 1 & 0 \end{matrix}] .$ $T P M # 2 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ - 1 & 0 \end{matrix}] .$

• The ‘Tx port l’/’Tx port 2’mapping: Used for mapping a single input to a single Tx port (SS 1 to Tx port 1 or SS 2 to Tx port 2)

$T P M # 3 = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}], T P M # 4 = [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}] .$ $T P M # 3 = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}], T P M # 4 = [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}] .$

• The ‘precoding’ mapping: Used for SM with precoding

$T P M # 5 = \frac{1}{\sqrt{2}} [\begin{matrix} e^{j φ} \cos θ & - e^{j φ} sinθ \\ sinθ & \cos θ \end{matrix}]; 0 \leq θ \leq \frac{π}{2}; 0 \leq φ < 2π .$ $T P M # 5 = \frac{1}{\sqrt{2}} [\begin{matrix} e^{j φ} \cos θ & - e^{j φ} sinθ \\ sinθ & \cos θ \end{matrix}]; 0 \leq θ \leq \frac{π}{2}; 0 \leq φ < 2π .$

• The ‘precoding without SS 2 input’/’precoding without SS 1 input’ mapping: Used in one of the modes of SM with precoding when only one input is present

$T P M # 6 = [\begin{matrix} e^{j φ} \cos θ & 0 \\ sinθ & 0 \end{matrix}], T P M # 7 = [\begin{matrix} 0 & - e^{j φ} sinθ \\ 0 & \cos θ \end{matrix}] 0 \leq θ \leq \frac{π}{2}; 0 \leq φ < 2π .$ $T P M # 6 = [\begin{matrix} e^{j φ} \cos θ & 0 \\ sinθ & 0 \end{matrix}], T P M # 7 = [\begin{matrix} 0 & - e^{j φ} sinθ \\ 0 & \cos θ \end{matrix}] 0 \leq θ \leq \frac{π}{2}; 0 \leq φ < 2π .$

12.4.3.6 Bit Allocation and Tx Port Mapping Allocation Table

In G.hn MIMO, the concept of BAT is expanded to include not only the variable bit loading (modulation) per subcarrier but also the Tx port mapping associated with each subcarrier. The Bit Allocation and Tx Port Mapping Allocation Table (BMAT) is the combination of the following elements:

1. The BATs for the payload of the PHY frame:

a. The BAT of SS 1, BAT⁽¹⁾

b. The BAT of SS 2, BAT⁽²⁾

2. The MAT for the payload of the PHY frame

The MAT is a vector associating each subcarrier index along the frequency axis with a specific Tx port mapping (i. e. a TPM matrix) to be used for this subcarrier. A specific BMAT is associated with an index called BMAT_ID.

The receiver is calculating the BMAT (i.e. the combination of both BATs and MAT) during the process of channel estimation and conveys this information to the transmitter using a specific ‘channel estimation’ management message. A transmitter may hold several BMATs with every receiver it communicates with. The specific BMAT used by the transmitting node in a particular PHY frame is indicated to the receiving node by a BMAT_ID field in the PFH.

FIGURE 12.20
Block diagram of the MIMO OFDM modulator for transmit stream (k). (Based on figure 7-10 from ITU-T. 2011. G.9963, Unified high-speed wireline-based home networking transceivers – Multiple input/multiple output specification. With permission.).

12.4.3.7 OFDM Modulator (Including Cyclic Shift on the Second Tx Port)

A MIMO transceiver comprises two OFDM modulators, one for each one of the two Tx ports. The OFDM modulator of an individual Tx port is modified compared to that of a legacy G.hn transceiver by introducing a new functional block which performs a cyclic shift on the two transmit streams. The block diagram for the OFDM modulator of an individual Tx port is given in Figure 12.20.

The cyclic shift cyclically shifts the samples of an OFDM symbol at the output of the IDFT, $y_{n, l}^{(k)}$ $y_{n, l}^{(k)}$ ), to generate a shifted version of this sequence, $x_{n, l}^{(k)}$ $x_{n, l}^{(k)}$ . This shift depends on both the transmit stream index and symbol type (preamble, PFH, ACE and payload). This operation is defined by the following equation:

$x_{n, l}^{(k)} = y_{(n - C S_{l}^{(q)}) \mod N, l}^{(k)} = \sum_{i = 0}^{N - 1} z_{i, l}^{(k)} \times \exp (j \cdot 2 π \cdot i \frac{n - C S_{l}^{(k)}}{N}), for n = 0,1, \dots, N - 1, and k = 1,2,$ $x_{n, l}^{(k)} = y_{(n - C S_{l}^{(q)}) \mod N, l}^{(k)} = \sum_{i = 0}^{N - 1} z_{i, l}^{(k)} \times \exp (j \cdot 2 π \cdot i \frac{n - C S_{l}^{(k)}}{N}), for n = 0,1, \dots, N - 1, and k = 1,2,$

where $C S_{l}^{(k)}$ $C S_{l}^{(k)}$ is the cyclic shift used for the lth OFDM symbol of the kth transmit stream. The values of the cyclic shift for the two transmit streams and the different OFDM symbols are listed in Table 12.6.

12.4.3.8 AFEs, Mapping of Tx Ports to Power Lines Conductors and PSD Requirements

The MIMO transceiver comprises two AFEs, one for each one of the two Tx ports. The mapping of transmit streams (Tx ports) to an actual combination of conductors (e.g. Tx port 1 connects to the P-N wire pair) is not specified in the G.hn MIMO specifications and is vendor discretionary. However, this mapping cannot change once a node is registered to a domain.

TABLE 12.6

Cyclic Shift Values

Source: Based on table 7-15 from ITU-T. 2011. G.9963, Unified high-speed wireline-based home networking transceivers – Multiple input / multiple output specification. With permission.

For a G.hn MIMO transceiver, the PSD requirements are that the sum of PSDs of the two transmit signals transmitted from the two Tx ports at any frequency shall never exceed the transmit PSD mask specified for single-port transmissions (see Section 12.2.4.5.10).

12.4.4 G.hn MIMO Payload Transmission Schemes

A G.hn MIMO transceiver is capable of transmitting using two transmission options:

1. Transmissions in which the payload is created as a single SS. This is used for several cases in which the ‘full MIMO scheme’, that is, the scheme which uses 2 SSs cannot be used. This includes cases in which a G.hn MIMO node transmits (unicast) to a legacy (non-MIMO) G.hn node or transmits to a multicast or broadcast group of nodes which includes such legacy nodes. Another case is a case in which the power lines installation does not include a third conductor (certain geographies do not include the ground/protective earth conductors). There are several variants for performing such transmissions. Further details on this option are given in Section 12.4.4.1.

2. Transmissions in which the payload is created as two SSs. These transmission schemes are used for transmissions between MIMO G.hn nodes and are aimed at exploiting the spatial diversity of the MIMO PLC channel to its full extent. The various possible schemes for such transmissions are described in Section 12.4.4.2.

In general, the selection between the various transmission options (transmission schemes) is usually in the hands of the receiver which is the side that has the knowledge of the MIMO channel response. The receiver performs the selection using management messages, of the ‘channel estimation’ protocol, which it sends to the transmitter In the case of transmissions in which the payload is created as a single SS, the transmitter has two transmission options and the selection between the two is in its hands, as described in Section 12.4.4.1 (both options are decodable by legacy G.hn nodes).

12.4.4.1 Payload Transmitted as a Single Spatial Stream (Transmission to Legacy G.hn Nodes)

Transmissions from a G.hn MIMO node in which the payload is created as a single SS can be done in two possible ways:

1. Transmission as specified in the legacy (non-MIMO) G.hn specifications (although these are single Tx port transmissions, several ‘semi-MIMO’ options are covered by this, as described in Section 12.4.1). (Clarification note: Although the term ‘SS’ is not explicitly defined in the legacy G.hn specifications, in essence, the legacy G.hn transmissions are single SS transmissions.)

2. A MIMO transmission (using the MIMO PHY frame) in which the payload is created as a single SS and duplicated for transmission over the two Tx ports simultaneously (with cyclic shift on the second port).

Transmissions according to both of these options will be decodable by legacy (non-MIMO) G.hn nodes. However, since the second option is actually a sort of transmit diversity transmission scheme, using it instead of the previous one (single Tx port transmission) is expected to provide improved performance with increased coverage when a G.hn MIMO node is transmitting to a legacy (non-MIMO) G.hn node.

The G.hn MIMO node needs to select one of the previously mentioned transmission rules to legacy devices, at the time of registration, and does not change this decision as long as it is still registered. A node may select a different transmission rule if it resigns from a domain and reregisters to the domain. The intention behind this is that since the transmission rule for a given legacy node does not change from frame to frame; the channels perceived by other nodes in the domain are consistent from frame to frame.

12.4.4.2 Payload Transmitted as Two Spatial Streams (Transmissions between G.hn MIMO Nodes)

A G.hn MIMO node transmitting to other G.hn MIMO nodes, and wanting to fully exploit the full spatial diversity of the MIMO PLC channel, will use transmission schemes in which the payload is created as two SSs. The G.hn specifications include three optional transmission schemes for this case:

1. Two variants of an SM MIMO with precoding, detailed in Section 12.4.4.2.1. This section also explains the difference between the two variants

2. SM MIMO without precoding (open-loop MIMO)

Selection between these schemes is at the hands of the receiver, indicating the requested ‘MIMO mode’ in the ‘channel estimation’ management messages it sends to the transmitter. The G.hn specifications include these options in order to allow a variety of implementation possibilities. Each of the schemes has its strengths and weaknesses. Typically a G.hn node vendor will implement one of the schemes taking into considerations practical considerations such as complexities in the receiver and transmitter, memory requirements and performance gains.

In OFDM systems, MIMO can be applied on a subcarrier level. One of the interesting and unique features of MIMO transmissions with two SSs, in G.hn, which cannot usually be found in wireless MIMO OFDM systems, is that this capability is really put into practice, by allowing the G.hn MIMO receiver to control the MIMO Tx port mapping, that is, deciding whether to transmit on one/two ports and with/without precoding, and conveying the precoding parameters (if used), on a per subcarrier basis, in addition to the ability to control the bit loading (modulation) of the transmitted signal on a per subcarrier basis.

12.4.4.2.1 Spatial Multiplexing MIMO with Precoding in G.hn MIMO

This section describes the SM MIMO scheme with precoding (or shortly, the ‘precoding scheme’) as implemented in the G.hn MIMO specifications. This scheme actually includes two operational modes as described hereafter. Some practical issues needs to be solved when devising this scheme, which was theoretically described in Section 12.3.4.1.

12.4.4.2.1.1 Feedback Format There are several options for an explicit feedback of channel state information from the receiver to the transmitter:

• Non-compressed feedback: Feeding back either the full channel response matrix, H, or the full precoding matrix V.

• Compressed feedback: Feeding back only the precoding matrix, V. There are also several options for a compressed feedback:

• Angle-based (parametric) approach: Due to the fact that V is a unitary matrix, it can be fully described with just two coefficients. There are different options for the definition of the two coefficients that build the matrix, for example, sending an amplitude and phase or sending two angles, as described later on.

• Codebook-based approach: In this approach, the precoding matrix is quantised and a look-up-table (LUT) of quantised precoding matrices is prepared (this is the ‘codebook’). The receiver selects the quantised precoding matrix that is closest (according to some error metric) to the calculated one and sends the index of this matrix in the LUT. The codebook is designed so that some error metric is minimised (usually the SNR degradation).

The approach selected for G.hn MIMO is the compressed feedback with an angle-based (parametric) approach. The major reasoning behind this selection is as follows:

• Using a non-compressed feedback usually reduces the efficiency of the MIMO scheme since the amount of information conveyed as feedback from the receiver to the transmitter is considerable; therefore, a compressed feedback is preferable.

• Comparing the compressed approaches (parametric vs. codebook-based approaches),

• The difference between the two lies in the fact that in the parametric approach, the parameters are quantised directly, which may not give a uniform bound for the SNR degradation, while in the codebook approach, construction of the codebook tries to uniformly bound this error (which may result in codebook entries which are non-uniformly spaced). Potentially, the codebook approach requires less feedback bits for the same quality.

• Practically, the codebook approach suffers from the following:

– Creating a codebook is not a trivial task. It requires a large measurement database which will cover different geographies. It is not obvious that a single codebook can achieve good results in different installations, geographies, etc.

– Complexity in the transmitter: The ‘codebook-based’ scheme requires storage of the codebook in the transmitter. Based on the size of the codebook, this can be a substantial amount of memory. The ‘angle-based’ scheme requires a negligible amount of memory at the transmitter (the precoding matrix can be calculated on-the-fly).

– Complexity in the receiver: In the ‘codebook-based’ scheme, the receiver performs a complex, exhaustive search of the best fitting precoder among the codebook. In order to achieve reasonable performance, the codebook will need to be very large, which would make this search impractical.

• For the parametric approach, several parametric representations were checked, such as magnitude/phase and log-magnitude/phase. These turned out to exhibited inferior performance relative to the representation with two angles.

The precoding matrix (per subcarrier), that is, the matrix used for Tx port mapping in the G.hn MIMO transmitter, is identical to the matrix specified in IEEE Std802.11n, defined by the Givens rotation, for the special case of a 2 × 2 matrix. The precoding matrix, per a single subcarrier (usually for the cases where the bit loading for the two SSs is non-zero), is defined by the angles Λ and φ:

Practically, the receiver sends the transmitter, a vector containing the pair of angles (θ, φ) for each subcarrier in the OFDM symbol. The transmitter uses these angles, reconstructs the precoding matrix and precodes the transmitted data on each subcarrier using the appropriate matrix.

12.4.4.2.1.2 Quantisation of the Angles The angles θ and φ are quantised to B₁ and B₂ bits, respectively. G.hn MIMO specifies two possible quantisation levels of either B₁ = B₂ = 4 bits or B₁ = B₂ = 8 bits. The quantisation level is selected by the receiver and applies to all of the precoding parameters (i.e. all of the subcarriers) in a single ‘channel estimation’ message used to deliver the precoding feedback for a set of subcarriers. The quantisation level is indicated in this message. Each message (feedback) can use a different quantitation level. The communication of the angle indices and quantisation level is described hereafter. Reconstructing the precoding matrix in the transmitter will be done in the following way: Given phase indices P₁ and P₂ for θ and φ, respectively, $0 \leq P_{1} \leq 2^{B_{1}} - 1$ $0 \leq P_{1} \leq 2^{B_{1}} - 1$ ; $0 \leq P_{2} \leq 2^{B_{2}} - 1$ $0 \leq P_{2} \leq 2^{B_{2}} - 1$ , for some subcarrier, the transmitter uses the mentioned precoding matrix, in which

$θ = \frac{π \cdot (2 P_{1} + 1)}{2^{B_{1} + 2}}, φ = \frac{π \cdot (2 P_{2} + 1)}{2^{B_{2}}} .$ $θ = \frac{π \cdot (2 P_{1} + 1)}{2^{B_{1} + 2}}, φ = \frac{π \cdot (2 P_{2} + 1)}{2^{B_{2}}} .$

12.4.4.2.1.3 Precoding Grouping Grouping of precoding parameters is very similar to the G.hn bit-loading (BAT) grouping. Precoding grouping decimates the amount of feedback (angles) sent in the reverse channel: instead of sending 2 angles per subcarrier, the feedback includes a single set of 2 angles per a group of subcarriers. This is in addition to the bit-loading grouping (i.e. the precoder group size PG may be different than the bit-loading group size G).

Precoding grouping, as other precoding parameters, is determined by the receiver. Clearly, this factor should be considered along with the quantisation issue. For example, a precoding feedback scheme that uses quantisation of (8, 8) for the two precoder angles (θ, φ) and precoding grouping of PG = 2 will probably outperform a feedback scheme with quantisation of (4, 4) and no precoding grouping, though both consume the same feedback rate.

One difficulty with precoding grouping is incurred by the cyclic shift applied to the 2nd transmit stream (Tx port). This cyclic shift imposes a rather large variation of the precoder parameters between adjacent subcarriers (the precoder parameters are not smooth), and consequently, a simple grouping scheme in which the same parameterisation of the precoder is used for a group of subcarriers is not feasible.

Let’s assume that without applying the cyclic shift, the channel matrix response, H, at a given subcarrier, admits the SVD H = UDV^H, where the precoder matrix V is indexed on two angles:

$V (θ,φ) = [\begin{matrix} e^{j φ} \cos θ & - e^{j θ} sinθ \\ sinθ & \cos θ \end{matrix}] .$ $V (θ,φ) = [\begin{matrix} e^{j φ} \cos θ & - e^{j θ} sinθ \\ sinθ & \cos θ \end{matrix}] .$

When a cyclic shift is used on the second Tx port, we get the equivalent channel:

$\tilde{H} = H [\begin{matrix} 1 & 0 \\ 0 & e^{j k α} \end{matrix}],$ $\tilde{H} = H [\begin{matrix} 1 & 0 \\ 0 & e^{j k α} \end{matrix}],$

where e^jkα accounts for the cyclic shift (linear phase) on the kth subcarrier. (Practically ${α = 2}^{*} π^{*} T_{C S} * F_{S C} = 0.098175$ ${α = 2}^{*} π^{*} T_{C S} * F_{S C} = 0.098175$ radians, where T_CS is the cyclic shift in time units and F_SC is the sub-carrier frequency spacing.) Now, using the decomposition of the original channel, we have

$\begin{array}{l} \tilde{H} = H [\begin{matrix} 1 & 0 \\ 0 & e^{j k α} \end{matrix}] = U D V^{H} (θ,φ) [\begin{matrix} 1 & 0 \\ 0 & e^{j k α} \end{matrix}] = U D {[\begin{matrix} e^{j φ} \cos θ & - e^{j φ} sinθ \\ sinθ & \cos θ \end{matrix}]}^{H}, \\ = e^{j k α} U D {[\begin{matrix} e^{j (φ+kα)} \cos θ & - e^{j (φ+kα)} sinθ \\ sinθ & \cos θ \end{matrix}]}^{H} = e^{j k α} U D V^{H} (θ,φ+ k α) . \end{array}$ $\begin{array}{l} \tilde{H} = H [\begin{matrix} 1 & 0 \\ 0 & e^{j k α} \end{matrix}] = U D V^{H} (θ,φ) [\begin{matrix} 1 & 0 \\ 0 & e^{j k α} \end{matrix}] = U D {[\begin{matrix} e^{j φ} \cos θ & - e^{j φ} sinθ \\ sinθ & \cos θ \end{matrix}]}^{H}, \\ = e^{j k α} U D {[\begin{matrix} e^{j (φ+kα)} \cos θ & - e^{j (φ+kα)} sinθ \\ sinθ & \cos θ \end{matrix}]}^{H} = e^{j k α} U D V^{H} (θ,φ+ k α) . \end{array}$

The previous derivation implies that given the cyclic-shift-free precoder parameterisation (θ, φ), when the cyclic shift (linear phase of kα) is applied, the counterpart precoder parameters are given by (θ, φ + kα). This new parameterisation actually counteracts the cyclic shift. Consequently, the G.hn MIMO specifications specify that if grouping is used, the parameterisation of the precoder, (θ, φ), that the receiver communicates to the transmitter refer to the first subcarrier in the group, and the transmitter should use the following precoder parameterisation (with compensation for the cyclic shift) for the group of PG subcarriers: (θ, φ), (θ, φ+α), …, (θ, φ+(PG–1)α), where PG denotes the precoding group size.

12.4.4.2.1.4 Two Precoding Modes (Treating Specific Subcarriers Which Have Bit Loading on Only One SS) As mentioned earlier, the G.hn MIMO specifications actually include two variants of the ‘SM MIMO scheme with precoding’. The difference between the two variants (called in the G.hn MIMO specifications ‘MIMO mode 1’ and ‘MIMO mode 2’) is in the way they treat specific subcarriers for which the bit loading (BAT) tells the transmitter, for a specific subcarrier, to load bits only on one SS related to that subcarrier (i.e. on the other SS of that subcarrier, zero bits are to be loaded). The Tx port mapping operation is described by

We are dealing with cases in which for a specific subcarrier i, zero bits have to be loaded on a specific SS q, that is, $b_{i}^{(q)}$ $b_{i}^{(q)}$ . In this case, $S_{i n, i}^{(q)}$ $S_{i n, i}^{(q)}$ . The difference between the two precoding variants (modes) is as follows:

1. In the first approach (‘MIMO mode 1’), the following matrices are used:

2. In the second approach (‘MIMO mode 2’), the following matrices are used:

$T P M # 3 = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}], T P M # 4 = [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}] .$ $T P M # 3 = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}], T P M # 4 = [\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}] .$

In each case, the first matrix is used when $b_{i}^{(2)}$ $b_{i}^{(2)}$ (i.e. loading on SS 2 is 0), and the second for the case when $b_{i}^{(1)}$ $b_{i}^{(1)}$ = 0 (i.e. loading on SS 1 is 0).

When a specific transmission (PHY frame) is using a specific mode out of the two modes previously described, this mode applies to the entire set of subcarriers (and the entire frame). This means that all subcarriers having bit loading of 0 on one of their SSs will follow the previous rule, according to the selected mode.

12.4.4.2.1.5 On Power Allocation The difference between the two precoding modes is that for the mentioned cases (in which, for a specific subcarrier, the bit-loading algorithm allocates zero bits to one SS and x bits to the other), in the first mode, all power is directed to a single SS, before applying the precoding matrix, while in the second mode, all power is directed to a single Tx port. The second mode is aimed to address potential concerns with the first mode: Although the first mode has the potential to achieve better performance than the second mode, the first mode might be violating radiation regulations. This is since in this mode, transmissions through the two Tx ports are correlated, and using full power on one of the SSs in this case might result (in some point in space) in a radiated power which is larger than that radiated from a single transmit port system by a factor that may reach 3 dB (this is in contrary to transmissions with the unitary precoding matrix and equal power of the SSs, which result in uncorrelated and equal-power transmit streams). Statistical probabilities of increased radiations (backed by field measurements) are discussed in Chapter 16. The second mode is more conservative by imposing the strict equivalent isotropically radiated power (EIRP) constraint (the sum of the absolute values of the transmitted signals through the two wire pairs should meet the total power, i.e. field strength, limitation). It can be shown that the optimum transmit strategy, for subcarriers with non-zero bit loading on a single SS, through multiple available transmit ports, under the EIRP constraint reduces to transmission through the Tx port with the largest transfer function for that subcarrier.

12.4.4.2.1.6 Virtual Grouping of the Tx Port Mappings Some receivers may implement payload-based channel estimation (e.g. decision-directed loops), which may be needed for various tracking purposes. For this kind of channel estimation process, frequency–domain smoothing of the channel estimates will be needed. This kind of smoothing requires that groups of subcarriers will use the same Tx port mapping (i.e. the same type of TPM matrix). For this reason, the specification provides means for the receiver to ask (optionally) the transmitter, to use either the unitary precoding matrix (TPM #5) or the matrices unique to mode 1 (TPM #6 and TPM #7) and mode 2 (TPM #3 and TPM #4), on groups of subcarriers. If this is indeed asked by the receiver, a group using (only) the unitary precoding matrix (TPM #5) will use it even for those subcarriers which have bit loading on only one SS. In this case, for those subcarriers, 2 random bits will be loaded from an LFSR (the one described in Section 12.4.3.4) on the SS with zero bit loading. An illustration of this feature is given in Figure 12.21, with an example of the Tx port mapping for the case of MIMO mode 2. In this example, the receiver is using virtual Tx port mapping grouping of 4 subcarriers in a group (the grouping is done implicitly by the receiver asking the transmitter for the same TPM for consecutive groups of subcarriers). The example shows a snapshot of the subcarrier axis, where the receiver asked for a ‘MIMO’ group followed by a ‘single Tx port’ group and another ‘MIMO’ group. The ‘MIMO’ group is a group of subcarriers which are using TPM #5 (the precoding matrix with equal power on the two Tx ports), and the ‘single Tx port’ group is using TPM #4 (per each subcarrier the bits of SS2 are mapped to Tx port 2, where full power is allocated to Tx port 2, while no power is allocated to Tx port1). The example also shows specific subcarriers within a ‘MIMO’ group which have zero bit loading on one SS but are still using TPM #5.

FIGURE 12.21
Tx port mapping example for MIMO mode 2. With virtual grouping of Tx ports mapping.

There is of course a trade-off between the need to group subcarriers in order to allow frequency–domain smoothing (with the performance gains that this mechanism gives) and the loss of theoretical performance incurred by this grouping (since, performance-wise, the optimal approach is to use an independent Tx port mapping on each subcarrier). This is a choice left for the implementer to decide on.

12.4.4.2.1.7 Channel Estimation Message Conveying the MIMO Scheme Parameters to the Transmitter The receiver, estimating the MIMO channel response, determines the MIMO configuration to be used by the transmitter (1 or 2 SSs, SM with/without precoding, and the precoding mode, if precoding is used), and its related parameters, and sends this information to the transmitter. This information is conveyed to the transmitter as part of the channel estimation protocol via special channel estimation management messages. This feedback, including the following information, in the case of SM MIMO with precoding, is as follows:

• A MIMO ‘mode’ indicator: Indicating MIMO mode 1 or 2 (SM with precoding) or MIMO mode 0 (SM without precoding)

• The BMAT which includes

• The two BATs for the two SSs

• The MAT, that is, matrices indices for all subcarriers (practically this is encoded as part of the two BATs)

• Bit-loading grouping (G)

• Precoding angles for all subcarriers

• Precoding grouping (PG)

12.4.4.2.2 Spatial Multiplexing MIMO without Precoding in G.hn MIMO

The SM MIMO scheme without precoding, specified in G.hn MIMO, is a vertical SM scheme (see Section 12.3.4.2). This mode is called ‘MIMO mode 0’ in the G.hn MIMO specifications. This scheme uses either equal-power MIMO transmission per subcarrier or transmission through a single port per subcarrier. In other words, the following matrices are assigned, per subcarrier, as Tx port mappings:

1. For subcarrier i, for which the bit loading for the two SSs is non-zero, that is, $b_{i}^{(q)} > 0$ $b_{i}^{(q)} > 0$ (q = 1, 2), the following matrix is used:

$T P M # 0 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] .$ $T P M # 0 = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] .$

This matrix connects SS 1 to Tx port 1 and SS 2 to Tx port 2, with equal power (in each port the power is 3 dB less than the full ‘single Tx port’ power). Note: This mapping is also used for subcarriers for which the bit loading is zero for either of the SS, in case the receiver works with the virtual Tx port mapping feature (explained further on), and this subcarrier belongs to a ‘MIMO’ group of subcarriers.

2. For subcarrier i, with zero bit loading on one of the SSs (i.e. $b_{i}^{(q)} > 0$ $b_{i}^{(q)} > 0$ for either q = 1 or 2), the following matrices are used (unless virtual Tx port mapping is used and these subcarriers are part of a ‘MIMO’ group):

The first matrix is used when $b_{i}^{(2)}$ $b_{i}^{(2)}$ = 0 (i. e. loading on SS 2 is 0), and the second for the case when $b_{i}^{(1)}$ $b_{i}^{(1)}$ = 0 (i.e. loading on SS 1 is 0). These matrixes direct all of the power to a single Tx port.

12.4.4.2.2.1 On Power Allocation The described scheme mixes subcarriers with ‘two Tx ports’ transmissions (with equal power on each port and in each port the power is 3 dB less than the full ‘single Tx port’ power) and subcarriers with ‘single Tx port’ transmissions (where the full power is placed in a single Tx port). This mix is actually a simple and pragmatic mechanism to achieve an approximate ‘waterfilling’ power allocation (without a need for the receiver to communicate the power allocation to the transmitter per subcarrier) which approaches the capacity of the optimal MIMO system (provided that ‘optimal’ MIMO decoding is used).

12.4.4.2.2.2 Virtual Grouping of the Tx Port Mappings

As explained for the precoding scheme, a G.hn MIMO receiver can ask the transmitter to use Tx port mappings which allocates the same type of TPM to groups of subcarriers. For the SM MIMO without precoding scheme, this means that the MAT will be composed of groups of subcarriers, and each group will use either matrix TPM #0 or the single Tx port matrices (TPM #3 and TPM #4).

12.4.4.2.3 Channel Estimation Message Conveying the MIMO Scheme Parameters to the Transmitter

In the case of SM MIMO without precoding, the following parameters are conveyed:

• The MIMO ‘mode’ indicator, indicating MIMO mode 0

• The BMAT which includes

• The two BATs for the two SSs

• The MAT, that is, matrices indices for all subcarriers (practically this is encoded as part of the two BATs)

• Bit-loading grouping (G)

12.5 Conclusions

The G.hn home networking technology was reviewed, with an emphasis on the G.hn MIMO enhancement. While a ‘regular’ G.hn transceiver transmits and receives over a single Tx and Rx port (usually a port is connected to a power line wire pair, e.g. the P-N pair), a G.hn MIMO transceiver allows transmission and reception on multiple Tx and Rx ports. This enhancement provides increased throughput and coverage, not only for G.hn MIMO transceivers communication with other G.hn MIMO transceivers but also when these transceivers communicate with non-MIMO G.hn transceivers.

G.hn MIMO transceivers can operate using several schemes. All of these schemes provide full interoperability with non-MIMO G.hn nodes, so that G.hn home networks may have a mix of MIMO and non-MIMO nodes. Following is a short summary of the possible transmission schemes:

For transmission to non-MIMO G.hn nodes, a G.hn MIMO node can use the following two schemes:

• A non-MIMO G.hn transmission (i. e. the same transmission format used by non-MIMO G.hn transceivers)

• A MIMO transmission in which the payload is created as a single SS which is duplicated and transmitted over the two Tx ports, with a cyclic shift applied to the second port

For transmissions between G.hn MIMO nodes, the G.hn MIMO transmitter will usually use a MIMO transmission scheme in which the payload is created as two SSs and transmitted over two Tx ports. In this case, the MIMO transmission will be done following one of three possible modes:

• MIMO mode 0: SM MIMO without precoding. This is an open-loop mode in which the transmitter independently transmits the two SSs over the two Tx ports (without any feedback from the receiver about the channel).

• MIMO modes 1 and 2: SM MIMO with precoding. These two modes are closed-loop modes in which the receiver conveys channel information to the transmitter. The transmitter uses this feedback information to ‘precode’ its transmitted data, so that the transmission is optimally adapted to the eigenmodes of the MIMO channel. The two modes differ in the way they handle specific subcarriers with bit loading on only one of the SSs, as explained in Section 12.4.4.2.1.

Table 12.7 summarizes the usage of the TPMs, used on a per subcarrier basis, for the different MIMO transmission mode.

In Table 12.7, the first line includes the cases in which the bit loading on a single subcarrier is greater than zero for both of the SSs (the bit loading on each SS in these cases can range between 1 to 12 bits). For these subcarriers, the payload bits (after the SS parser) are mapped to the two Tx ports using either the SM with precoding matrix (TPM #5) if MIMO modes 1 or 2 are used or the identity matrix (TPM #0) for SM without precoding if MIMO mode 0 is used.

The first line in Table 12.7 also includes cases in which the bit loading on a specific subcarrier, on at least one SS, is zero, and the receiver chooses to use TPM #5 or TPM #0 (depending on the MIMO mode) for this subcarrier. For this subcarrier, two random bits are loaded from an LFSR on the SSs with zero bit loading. This feature was referred to as virtual grouping of the Tx port mappings and is useful for cases where the receiver is performing frequency–domain smoothing of channel estimates on a group of subcarriers. In this case if most of the subcarrier in the group has bit loadings different than zero, the receiver will ask the transmitter that all of the subcarriers in this group (called a ‘MIMO group’) will use mappings of TPM #5 or TPM #0, even for those single subcarriers within the group where the bit loading on one or two SSs is zero.

TABLE 12.7

Usage of TPMs for the Different MIMO Modes Used for MIMO Payload Transmissions (No. of SSs = 2)

		MIMO Modes
Bit Loading for the Two Spatial Streams		SM w/o Precoding	SM with Precoding
SS 1	SS 2	Mode 0	Mode 1	Mode 2
0 ≤ x₁ ≤ 12	0 ≤ x₂ ≤ 12	TPM #0	TPM #5	TPM #5
x₁ = 0	0 ≤ x₂ ≤ 12	TPM #4	TPM #7	TPM #4
0 ≤ x₁ ≤ 12	x₁ = 0	TPM #3	TPM #6	TPM #3

Source: Based on table 8-2 from ITU-T. 2011. G.9963, Unified high-speed wireline-based home networking transceivers – Multiple input/multiple output specification. With permission.

Lines 2 and 3 in Table 12.7 include alternative Tx port mapping options for the cases in which the bit loading on a specific subcarrier, on one SS, is zero (an alternative which optimises the performance per these subcarriers on the expanse of not being able to perform the mentioned frequency–domain smoothing). In these cases the payload bits allocated to the SS with non-zero bit loading are mapped either to a single Tx port using TPM #3 or TPM #4 (depending on which SS is with non-zero bit loading) if MIMO modes 0 or 2 are used or through a degenerated precoding matrix (a precoding matrix with only the column matching the SS with non-zero bit loading) to the two Tx ports using TPM #6 or TPM #7 (depending on which SS is with non-zero bit loading) if MIMO mode 1 is used.

The two MIMO modes with precoding differ in the way they treat the cases of zero bit loading on a single SS for a specific subcarrier (subcarrier not included in ‘MIMO groups’ of subcarriers, if the virtual grouping of Tx port mappings option is used): MIMO mode 1 directs all of the power to a single SS, before applying the precoding matrix, while in MIMO mode 2, all power is directed to a single Tx port. Although mode 1 has the potential to achieve better performance than the second mode, it might be violating radiation regulations, while mode 2 is more conservative by imposing the strict EIRP constraint.

The open-loop and two closed-loop (precoding) modes provide the designer of the G.hn transceiver with flexibilities to allow different receiver complexities versus performance trade-offs. In addition, the MIMO transmission modes allows the receiver to control both the transmitted MIMO Tx port mapping (according to the specific MIMO mode use) and the bit loading on a per subcarrier basis, in a way which allows the receiver to perform frequency–domain smoothing of channel estimates (channel estimates derived from the payload).

The MIMO transmission format is such that the G.hn preamble and G.hn PFH are duplicated and transmitted over the two Tx ports (i. e. the preamble and PFH transmitted on the second Tx port are copies of the preamble and header symbol transmitted on the first Tx port), with cyclic shift applied to the transmissions on the second Tx port. An ACE symbol is added following the PFH to allow the receiver to obtain MIMO channel estimations. Transmissions following these schemes are on the one hand transparent to non-MIMO G.hn transceivers and on the other hand provide the G.hn MIMO receiver with the ability to tune and train its AGC and other frame acquisition loops (timing, frequency, etc.) on a MIMO signal, on a frame-by-frame basis, in preparation for receiving the MIMO transmission of the payload.

References

1. ITU-T. 2010. G.9961. Unified high-speed wire-line based home networking transceivers – Data link layer specification.

2. ITU-T. 2012. G.9961 Amendment 1. Data link layer (DLL) for unified high-speed wire-line based home networking transceivers – Amendment 1.

3. ITU-T. 2011. G.9963. Unified high-speed wireline-based home networking transceivers – Multiple input/multiple output specification.

4. ITU-T. 2010. G.9964. Unified high-speed wireline-based home networking transceivers – Power spectral density specification.

5. Oksman V. and Galli S. October 2009. G.hn: The new ITU-T home networking standard. IEEE Communications Magazine, 47(10): 138–145.

6. ITU-T. 2010. G.9972. Coexistence mechanism for wireline home networking transceivers.

7. Schumacher L, Berger L.T, and Ramiro Moreno J. 2002. Recent advances in propagation characterisation and multiple antenna processing 430 in the 3GPP framework, in XXVIth URSI General Assembly, Maastricht, the Netherlands, August 2002, session C2. [Online] Available: http://www.ursi.org/Proceedings/ProcGA02/papers/p0563.pdf, accessed 29 September 2013.

8. Alamouti S.M. October 1998. A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications, 16(8): 1451–1458.

9. Gallager R. G. 1968. Information Theory and Reliable Communication. John Wiley & Sons, New York.

10. Lozano A, Tulino A.M. and Verdu S. 2006. Optimum power allocation for parallel Gaussian channels with arbitrary input distributions. IEEE Transactions on Information Theory, 52(7): 3033–3051.

11. Stadelmeier L. et al. 2008. MIMO for in home power line communications, in Seventh International ITG Conference on Source and Channel Coding (SCC 2008), Honolulu, HI.

12. ITU-T. 2011. G.9960. Unified high-speed wireline-based home networking transceivers – System architecture and physical layer specification.

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